## Mean weight of whole from sample size

I do not know how to do the following question:

“A fish wholesaler has a catch of several thousand lobsters. A prospective buyer selected 40 at random and obtained the following weights in ounces:

21.3, 21.1, 21.4, 18.8, 20.2, 19.3, 19.1, 18.3, 19.9, 22.0,

20.6, 20.7, 21.9, 20.1, 17.1, 19.3, 21.2, 18.4, 21.0, 21.6,

16.5, 18.9, 17.4, 20.8, 18.5, 18.1, 21.1, 19.3, 21.5, 20.1,

21.8, 20.2, 19.7, 18.9, 19.5, 20.0, 18.7, 21.6, 20.9, 21.5,

The prospective buyer will purchase the entire catch if it can be shown that the mean weight (of the entire catch) exceeds 19.9 ounces. Should he purchase the entire catch?”

## Hypothesis testing and significance test for hypoglycaemia

Rachel’s doctor suspects she is suffering from hypoglycaemia. The amount of glucose in the bloodstream varies and a person with hypoglycaemia has an average blood glucose level of less than 65 mg/dL. To determine whether Rachel is indeed hypoglycaemic the doctor sends her home with a glucose monitor to test her blood at 40 random times throughout the week.

a. Set up hypotheses to help determine if Rachel is hypoglycaemic.

b. Why did her doctor have her test her blood glucose level 40 times?

c. What would a Type I error be in the context of this situation?

d. What would a Type II error be in the context of this situation?

e. The results from the week of testing were x = 60.5mg/dL and s = 12.3 mg/dL. Conduct a significance test and give Rachel a diagnosis about hypoglycaemia.

## Proportion of Sample Who Enjoy Shopping

Sample question:

A sample of 500 shoppers were selected in a large metropolitan to determine various information concerning consumer behavior. Among the questions asked was, “Do you enjoy shopping for clothing?”

The results are summarized in the following contigency table:

Enjoy Shopping for Clothing MALE FEMALE TOTAL

YES 136 224 360

NO 104 36 140

TOTAL 240 260 500

a) Is there evidence of a significant difference between the proportion males and females who enjoy shopping for clothing at the 0.01 level of significance?

b) Determine the p-value in (a) and interpret its meaning

c) What are your answers to (a) and (b) if 206 males enjoyed shopping for cloting and 34 did not?

## Hypothesis Tests Related to Real Life Decisions

In your environment (business or personal), please describe a hypothesis test related to a decision. What would be your data? What would be your null hypothesis? What would be your alternate hypothesis? What would be your Type 1 and Type 2 errors relative to your decision? Suppose you have a p-value of 0.01, what does this mean relative to your problem and decision? Suppose the p-value is 0.20, what does this mean relative to your problem and decision?

## HYPOTHESIS TESTING: Null Hypothesis Relative to Problem and Decision.

In your environment (business or personal), please describe a hypothesis test related to a decision. What would be your data? What would be your null hypothesis? What would be your alternate hypothesis? What would be your Type 1 and Type 2 errors relative to your decision? Suppose you have a p-value of 0.01, what does this mean relative to your problem and decision? Suppose the p-value is 0.20, what does this mean relative to your problem and decision?

## Critical Thinking Statistical Analysis of an Article

Critical Thinking Concept Review

1. Choose three peer C-reviewed research articles and write a short review of each of them that includes the following:

a. Write the problem statement.

b. Name the theoretical model used or briefly describe the overall conceptual model.

c. Write out the main research questions. What is the rationale for the question?

d. List the main hypotheses that the study seems to be testing.

e. Define the dependent variable and the main independent variables.

f. Briefly describe the research design.

g. Describe the sample (e.g. size, sociodemographic characteristics) and how it was obtained.

h. List the statistics used to test the hypotheses.

i. Identify the main assumptions and limitations.

## Statistics: computerized tutorial center

A computerized tutorial center at a local college wants to compare two different statistical software programs. Students going to the center are matched with other student having similar abilities in statistics (assume the matching process creates matched pairs acceptable for use with the appropriate paired test statistic for the null hypothesis of no difference). A random sample of 10 student pairs is selected for each pair, one student is randomly assigned program A, the other program B.

After two weeks of using the program, the students are given an evaluation test. Their grades are:

Program A

64

68

75

97

90

55

68

64

91

95

Program B

62

72

79

57

91

56

88

89

77

76

Do the data provide evidence, at the 5% significance level, that there is a difference in mean student performance between the two software programs?

Assume that the population of all possible paired differences is approximately normally distributed. In support of your decision show the null and alternative hypothesis and the value of the test statistics computed for assessing the significance level.

## Using Statistics to Conclude is Performance is Independent of Time of Shift

Suppose that the medical staff indicates that the results of a given laboratory procedure must be available 30 minutes after the physician submits a request for the service. In this situation, if the results arrived 30 minutes or less after the request, we regard the performance of the laboratory as timely. If results arrived more than 30 minutes after the request, we regard the performance as tardy. Focusing on the day, evening, and night shifts, suppose that we selected a random sample and obtained the following results:

Shift

Performance Day Evening Night

Timely 100 80 40

Tardy 20 30 40

If 0.05, use these results to test the proposition that the performance of the laboratory is independent of shift. After finding standard deviation and mean, give a brief analysis of the description of the data set.

## Statistics help needed

1. A researcher collected data from 28 individuals. Seven independent variables were used to predict a dependent variable. The value of R2 for this model was .87. When the variable X_1 and X_3 were omitted from the model, R^2 was .84. Do the variables X1 and X3 contribute to the prediction of the dependent variable? Use a .10 significance level.

2. After a series of hurricanes struck Florida in 2004 and the price of oil exceeded $50 a barrel, the federal government negotiated with oil companies to lend them oil from the U.S. Strategic Petroleum Reserve. The market capitalization of major oil companies is mostly driven by their oil/ gas reserves. Suppose that an energy consultant collected data on 10 major oil companies to determine the relationship between an oil company’s reserves, X (in units of billions of barrels), and market capitalization, Y (in units of billions of dollars).

a. The R^2 for the regression equation Y= -18.035 + 10.856X is 91.78%. Test that the variable oil reserves contributes to the prediction of market capitalization. Use a 1% significance level.

b. The R^2 for the regression equation Y= -9.045 + 7.857X + .150X2 is 92.29%. Test that the variable oil reserves and the square of this variable contribute to the prediction of market capitalization. Use a 1% significance level.

c. What is the adjusted value of R^2 for the model in parts a and b? Since the value of the adjusted R&2 does not increase in value for the model in part b, what conclusion can you make about the appropriateness of adding the quadratic term to the model?

Solution Preview

## Statistics: Hypothesis and Error Types

In a specific company, there are three levels of workers: skilled, unskilled, and manager. The owner of this company wants to know if the level of job satisfaction differs amongst the three levels of workers.

Data: 30 workers in each level are randomly selected to take the job satisfaction survey. The survey asks each worker on a scale of 1-10 how satisfied he or she is with his or her job. The data will consist of 90 workers total (30 belonging to skilled, 30 belonging to unskilled, and 30 belonging to manager) and their satisfaction rating.

Null Hypothesis: The population means of satisfaction ratings of each of level of worker are equal to each other.

Alternative Hypothesis: The population means of satisfaction ratings of each of level of worker are not all equal to each other.

Type 1 Error: We incorrectly reject the null hypothesis that the population means of satisfaction ratings of each of level of worker are equal to each other.

Type 2 Error: We fail to reject the null hypothesis that the population means of satisfaction ratings of each level of worker are equal to each other even though the null hypothesis if false.

If we obtained a p-value a .2 from a test statistic, that means we have a 20 percent probability of obtaining a test statistic at least as extreme as our test statistic assuming the null hypothesis is true. At a .05 level of significance, we would fail to reject the null hypothesis.

If we obtained a p-value a .01 from a test statistic, that means we have a 1 percent probability of obtaining a test statistic at least as extreme as our test statistic assuming the null hypothesis is true. At a .05 level of significance, we would reject the null hypothesis.

a. Reformulate your hypothesis test to incorporate a 2-sample hypothesis test. What would be your data? What is your null hypothesis? What is your alternate hypothesis? What would be your Type 1 and Type 2 errors relative to your decision? Suppose you have a p-value of 0.01, what does this mean relative to your problem and decision? Suppose the p-value is 0.20, what does this mean relative to your problem and decision?

b.If you reformulated your design for 3 or more samples, what would be the implications of interaction? When would you use Tukey-Kramer test?

## Point Estimate of Statistics and Probability Calculation

1. A simple random sample of five months of sales data provided the following information

Month 1 2 3 4 5

Units Sold 94 100 85 94 92

a. Develop a point estimate of the population mean number of units sold per month.

b. Develop a point estimate of the population standard deviation

2. The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009):

Critical Reading 502

Mathematics 515

Writing 494

Assume that the population standard deviation on each part of the test is o = 100.

a. What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test?

b. What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test (to 4 decimals)?

c. What is the probability a random sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the writing part of the test (to 4 decimals)?

## Miscellaneus Statistics Questions

1. Assume there are 20 homes in the Quail Creek area and 10 of them have a security system. Four homes are selected at random:

(a) What is the probability all four of the selected homes have a security system? (Round your answer to 4 decimal places.)

(b) What is the probability none of the four selected homes have a security system? (Round your answer to 4 decimal places.)

(c) What is the probability at least one of the selected homes has a security system? (Round your answer to 4 decimal places.)

2. A study was conducted to determine if there was a difference in the humor content in British and American trade magazine advertisements. In an independent random sample of 278 American trade magazine advertisements, 69 were humorous. An independent random sample of 194 British trade magazines contained 34 humorous ads.

(a) State the decision rule for .05 significance level: H0: πA = πB; H1: πA ≠ πB. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

(b) Compute the value of the test statistic. (Do not round the intermediate values. Round your answer to 2 decimal places.)

3. According to a study by the American Pet Food Dealers Association, 62 percent of U.S. households own pets. A report is being prepared for an editorial in the San Francisco Chronicle. As a part of the editorial a random sample of 280 households showed 180 own pets. Does this data disagree with the Pet Food Dealers Association data? Use a 0.20 level of significance.

(a) State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.)

(b) State the decision rule for 0.20 significance level. (Round your answers to 2 decimal places.)

(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)

4. A United Nations report shows the mean family income for Mexican migrants to the United States is $28,540 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 28 Mexican family units reveals a mean to be $34,120 with a sample standard deviation of $10,050. Does this information disagree with the United Nations report? Apply the 0.01 significance level.

(a) State the null hypothesis and the alternate hypothesis.

(b) State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)

5.As part of an annual review of its accounts, a discount brokerage selects a random sample of 27 customers. Their accounts are reviewed for total account valuation, which showed a mean of $34,900, with a sample standard deviation of $8,300.

What is a 95 percent confidence interval for the mean account valuation of the population of customers? (Round your answers to the nearest dollar amount. Omit the “$” sign in your response.)

95 percent confidence interval for the mean account valuation is between___ $ and____ $ ?

6. An important factor in selling a residential property is the number of people who look through the home. A sample of 17 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 26 and the standard deviation of the sample was 7 people.

Develop a 90 percent confidence interval for the population mean. (Round your answers to 2 decimal places.)

Confidence interval for the population mean is between____ and____ ?

7. During a national debate on changes to health care, a cable news service performs an opinion poll of 490 small-business owners. It shows that 48 percent of small-business owners do not approve of the changes.

(a) Develop a 90 percent confidence interval for the proportion opposing health care changes. (Round your answers to 4 decimal places.)

Confidence interval for the proportion_____ and_____ .

8. In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.80 hours per week playing organized sports. The population’s standard deviation is 2.80 hours per week. Based on a sample of 100 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.

(a) Compute the standard error of the sample mean. (Round your answer to 2 decimal places.)

(b) What is the chance HLI will find a sample mean between 5 and 6.6 hours? (Round z and standard error values to 2 decimal places and final answer to 4 decimal places.)

(c) Calculate the probability that the sample mean will be between 5.5 and 6.1 hours. (Round z and standard error values to 2 decimal places and final answer to 4 decimal places.)

9. Keith’s Florists has 19 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 19 trucks, 6 have brake problems. A sample of 5 trucks is randomly selected. What is the probability that 2 of those tested have defective brakes? (Round your answer to 4 decimal places.)

10. According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,080. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $480. (Round z-score computation to 2 decimal places and your final answer to 2 decimal places. Omit the “%” sign in your response.)

(a) What percent of the adults spend more than $2,375 per year on reading and entertainment?

(b) What percent spend between $2,375 and $3,225 per year on reading and entertainment?

(c) What percent spend less than $1,175 per year on reading and entertainment?

## Computing value of test statistic

Consider the following hypothesis test:

Ho: u > 20 (( their is a line under this sine >))

Ha: u < 20

A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

a. Compute the value of the test statistic.

b. What is the p-value?

c. Using a = .05, what is your conclusion?

d. What is the rejection rule using the critical value? What is your conclusion?

And

Consider the following hypothesis test:

Ho: u = 22

Ha: u =22 ( their is a line throw the = sine hare )

A sample of 75 is used and the population standard deviation is 10. Compute the p-value

and state your conclusion for each of the following sample results. Use a = .01.

a. i = 23

b. i = 25.1

c. i = 20.

## Hypotheses Based on P-Value and Level of Significance

3. A survey taken showed that among 785 randomly selected subjects who completed 4 years of college, 144 smoke and 641 do not smoke (based on data from the American Medical Association). Use the 0.01 level of significance to test the claim that the rate (proportion) of smoking among those with four years of college is less than 27 out of 100 rate of the general public. Why do you think that the rate of college graduates who smoke would be less than the rate of the general public?

1. State the Null Hypothesis and the Alternative Hypothesis

2. Determine the test statistic.

3. Determine the P-value

4. Make a decision regarding the hypotheses based on the P-value and the Level of Significance.

## Concluding Mean Waiting Time and Premium Rate

The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posted answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of 12 minutes before being able to talk to an IRS employee. Suppose you select a sample of 50 callers after the new phone service has been implemented; the sample results show a mean waiting time of 10 minutes before an IRS employee comes on the line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting time is 8 minutes. Using your sample results, can you conclude that the actual mean waiting time turned out to be significantly less than the 12-minute claim made by the taxpayer advocate? Use ex = .05.

and

Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. A sample of 35 surveys provided the survey times shown in the file named Fowle. Based upon past studies, the population standard deviation is assumed known with a = 4 minutes. Is the premium rate justified?

a. Formulate the null and alternative hypotheses for this application.

b. Compute the value of the test statistic.

c. What is the p-value?

d. At a = .01, what is your conclusion?