Statistics - Excercise

1. Access the hourly wage data on the below Excel Data File (Hourly Wage). An economist wants to test if the average hourly wage is less than $29.

A) Select the null and the alternative hypotheses for the test. Please select one of the following.

A1)H0: μ = 29; HA: μ ≠ 29

A2) H0: μ ≤ 29; HA: μ > 29

A3) H0: μ ≥ 29; HA: μ < 29

B) Use the Excel function Z.TEST to calculate the p-value. Assume that the population standard deviation is $7. (Round your answer to 4 decimal places.)

C) At α = 0.05 what is the conclusion? Please select one of the following

C1) Do not reject H0; the hourly wage is not less than $29

C2)Do not reject H0; the hourly wage is less than $29.

C3)Reject H0; the hourly wage is not less than $29.

C4) Reject H0; the hourly wage is less than $29

2.A local bottler in Hawaii wishes to ensure that an average of 24 ounces of passion fruit juice is used to fill each bottle. In order to analyze the accuracy of the bottling process, he takes a random sample of 50 bottles. The mean weight of the passion fruit juice in the sample is 23.69 ounces. Assume that the population standard deviation is 0.87 ounce. Use Table 1.

Use the critical value approach to test the bottler's concern at α = 0.01.

A) Select the null and the alternative hypotheses for the test.Please select one of the following.

A1)H0: μ ≤ 24; HA: μ > 24

A2)H0: μ ≥ 24; HA: μ < 24

A3) H0: μ = 24; HA: μ ≠ 24

B) Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

C) Find the critical value(s). (Round your answer to 2 decimal places.)

D) What is the conclusion? Please select one of the following.

D1)Do not reject H0 since the value of the test statistic is less than the negative critical value.

D2)Do not reject H0 since the value of the test statistic is not less than the negative critical value.

D3)Reject H0 since the value of the test statistic is less than the negative critical value.

D4) Reject H0 since the value of the test statistic is not less than the negative critical value.

E) Make a recommendation to the bottler

The accuracy of the bottling process is not compromised or compromised.

3. A politician claims that he is supported by a clear majority of voters. In a recent survey, 22 out of 42 randomly selected voters indicated that they would vote for the politician. Use a 1% significance level for the test. Use Table 1.

A) Select the null and the alternative hypotheses. Please select one of the following.

A1)H0: p = 0.50; HA: p ≠ 0.50

A2)H0: p ≤ 0.50; HA: p > 0.50

A3) H0: p ≥ 0.50; HA: p < 0.50

B) Calculate the sample proportion. (Round your answer to 3 decimal places.)

C) Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

D)Calculate the p-value of the test statistic. (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and final answer to 4 decimal places.)

E) What is the conclusion? Please select one of the following

E1)Reject H0; the politician is supported by a clear majority

E2)Reject H0; the politician is not supported by a clear majority

E3)Do not reject H0; the politician is supported by a clear majority

E4)Do not reject H0; the politician is not supported by a clear majority

4.You would like to determine if more than 45% of the observations in a population are below 10. At α = 0.01, conduct the test on the basis of the following 20 sample observations: Use Table 1.

6	6	12	6	5	9	6	14	6	13
10	12	8	14	8	8	13	13	8	8

A) Select the null and the alternative hypotheses. Please select one of the following.

A1)H0: p ≤ 0.45; HA: p > 0.45

A2)H0: p = 0.45; HA: p ≠ 0.45

A3) H0: p ≥ 0.45; HA: p < 0.45

B)Calculate the sample proportion. (Round your answer to 2 decimal places.)

C) Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

D) Calculate the p-value of the test statistic. (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and final answer to 4 decimal places.)

E) What is the conclusion? Please select one of the following.

E1)Reject H0 since the p-value is smaller than α

E2)Reject H0 since the p-value is greater than α

E3)Do not reject H0 since the p-value is smaller than α.

E4)Do not reject H0 since the p-value is greater than α.

5.Consider the following hypotheses:

H0: μ = 33

HA: μ ≠ 33

The population is normally distributed. A sample produces the following observations:

37	36	34	34	38	36	30

Use the p-value approach to conduct the test at a 10% level of significance. Use Table 2.

A) Find the mean and the standard deviation. (Round intermediate calculations to 4 decimal places. Round your answers to 2 decimal places.)

B) Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

C) Approximate the p-value of the test statistic. Please select one of the following

C1)p-value < 0.02

C2)0.02 < p-value < 0.05

C3)0.05 < p-value < 0.10

D) What is the conclusion? Please select one of the following

D1)Do not reject H0 since the p-value is smaller than α.

D2) Do not reject H0 since the p-value is greater than α.

D3)Reject H0 since the p-value is smaller than α.

D4) Reject H0 since the p-value is greater than α

6. A retailer is looking to evaluate its customer service. Management has determined that if the retailer wants to stay competitive, then it will have to have at least a 92% satisfaction rate among its customers. Management will take corrective actions if the satisfaction rate falls below 92%. A survey of 1,470 customers showed that 1,323 were satisfied with their customer service. Use Table 1.

A) Select the hypotheses to test if the retailer needs to improve its services. Please select one of the following.

A1)H0: p ≤ 0.92; HA: p > 0.92

A2)H0: p ≥ 0.92; HA: p < 0.92

A3)H0: p = 0.92; HA: p ≠ 0.92

B) What is the value of the appropriate test statistic? (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

C) Compute the p-value. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

D) What is the conclusion?

The management will NOT take corrective action or management WILL take corrective action.

7) The margarita is one of the most common tequila-based cocktails, made with tequila, triple sec, and lime juice, often served with salt on the glass rim. A manager at a local bar is concerned that the bartender is not using the correct amounts of the three ingredients in more than 50% of margaritas. He secretly observed the bartender and found that he used the CORRECT amounts in only 15 out of the 46 margaritas in the sample. Use the critical value approach to test if the manager's suspicion is justified at α = 0.10. Let p represent the proportion of all margaritas made by the bartender that have INCORRECT amounts of the three ingredients. Use Table 1.

A) Select the null and the alternative hypotheses. Please select one of the following

A1)H0: p = 0.50; HA: p ≠ 0.50

A2)H0: p ≥ 0.50; HA: p < 0.50

A3)H0: p ≤ 0.50; HA: p > 0.50

B) Calculate the sample proportion. (Round your answer to 3 decimal places.)

C) Calculate the value of test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

D) Calculate the critical value. (Round your answer to 2 decimal places.)

E) What is the conclusion? Please select one of the following.

E1)The manager's suspicion is justified since the value of the test statistic falls in the rejection region.

E2)The manager’s suspicion is not justified since the value of the test statistic falls in the rejection region.

E3)The manager's suspicion is not justified since the value of the test statistic does not fall in the rejection region.

E4)The manager’s suspicion is justified since the value of the test statistic does not fall in the rejection region.

8. A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 92% reliable. In other words, if an individual lies, there is a 0.92 probability that the test will detect a lie. Let there also be a 0.040 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions.

A)What is the probability of Type I error? (Round your answer to 3 decimal places.)

B) What is the probability of Type II error? (Round your answer to 2 decimal places.)

9.Determine the critical values for the following tests of the population mean with an unknown population standard deviation. The analysis is based on 8 observations drawn from a normally distributed population at a 10% level of significance. Use Table 2. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

A) H0: μ ≤ 50 versus HA: μ > 50 What is the critical value?

B) H0: μ = 9.4 versus HA: μ ≠ 9.4 ± What is the critical value?

C) H0: μ ≥ 6.7 versus HA: μ < 6.7 What is the critical value?

D) H0: μ = 11 versus HA: μ ≠ 11 ± What is the critical value?

10.Consider the following hypotheses:

H0: μ ≥ 182

HA: μ < 182

A sample of 72 observations results in a sample mean of 173. The population standard deviation is known to be 21. Use Table 1.

A) What is the critical value for the test with α = 0.10 and with α = 0.05? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

B) Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

C) Does the above sample evidence enable us to reject the null hypothesis at α = 0.10?Please select one of the following

C1)Yes since the value of the test statistic is less than the negative critical value.

C2)No since the value of the test statistic is not less than the negative critical value.

C3)Yes since the value of the test statistic is not less than the negative critical value.

C4)No since the value of the test statistic is less than the negative critical value.

D) Does the above sample evidence enable us to reject the null hypothesis at α = 0.05? Please select one of the following

D1)Yes since the value of the test statistic is less than the negative critical value.

D2)No since the value of the test statistic is not less than the negative critical value.

D3)Yes since the value of the test statistic is not less than the negative critical value.

D4)No since the value of the test statistic is less than the negative critical value.

11. Consider the following hypotheses:

H0: μ = 380

HA: μ ≠ 380

The population is normally distributed with a population standard deviation of 80. Use Table 1.

A) Use a 1% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

B) Calculate the value of the test statistic with formula287.mml = 414 and n = 40. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

C) What is the conclusion at α = 0.01? Please select one of the following

C1)Do not reject H0 since the value of the test statistic is smaller than the critical value.

C2) Do not reject H0 since the value of the test statistic is greater than the critical value.

C3)Reject H0 since the value of the test statistic is smaller than the critical value.

C4) Reject H0 since the value of the test statistic is greater than the critical value

D) Use a 10% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

E) Calculate the value of the test statistic with formula287.mml = 351 and n = 40. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

F) What is the conclusion at α = 0.10? Please select one of the following.

F1)Reject H0 since the value of the test statistic is not less than the negative critical value

F2)Reject H0 since the value of the test statistic is less than the negative critical value.

F3)Do not reject H0 since the value of the test statistic is not less than the negative critical value.

F4) Do not reject H0 since the value of the test statistic is less than the negative critical value.

12. Consider the following hypotheses:

H0: μ ≥ 100

HA: μ < 100

The population is normally distributed. A sample produces the following observations:

88

77

100

83

102

96

Use the critical value approach to conduct the test at a 5% level of significance. Use Table 2.

A)Find the mean and the standard deviation. (Round intermediate calculations to 4 decimal places. Round your answers to 2 decimal places.)

B) Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

C) Calculate the critical value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 3 decimal places.)

D) What is the conclusion? Please select one of the following

D1)Do not reject H0 since the value of the test statistic is less than the negative critical value.

D2)Do not reject H0 since the value of the test statistic is not less than the negative critical value.

D3)Reject H0 since the value of the test statistic is less than the negative critical value.

D4)Reject H0 since the value of the test statistic is not less than the negative critical value.