Reference no: EM132286205

1.A waste management service attempts to design routes so that each of their trucks pick-up on average four tons of garbage or less. A garbage collector believes, however, that he averages picking up more than four tons of garbage per day and decides to perform a hypothesis test. 

If the hypothesis test is performed at a 5% significance level and the resulting p-value is 0.04. Your conclusion should be: 

a) Fail to reject H0 because the p-value is less than 0.05.

b) Reject H0 because the p-value is less than 0.05.

c) Accept H0 because the p-value is less than 0.05.

d) Fail to accept H0 because the p-value is less than 0.05.

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic t. 

2.A local newspaper reported that for the adult population of a town, the mean annual salary is $30,000. Test the claim that for the adult population of this town, the mean annual salary is greater than $30,000. Sample data are summarized as n = 17, sample mean = $22,298, and s = $14,200. Use a significance level of alpha = 0.05.

Find the test statistic t.  

a) -2.24

b) -1.57

c) 1.57

d) 2.24

e) 0.05

Assume a normal distribution and use a hypothesis test to test the given claim.

3.According to city reports, it was found that the mean age of the prison population in the city was 26 years. Marc wants to test the claim that the mean age of the prison population in his city is less than 26 years. He obtains a random sample of 25 prisoners and finds a mean age of 24.4 years and a standard deviation of 9.2 years. At a significance level of 0.05, what should his conclusion be?

Note: The p-value = 0.1966.

a) Do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.

b) Reject the null hypothesis. The evidence suggests that the mean age is less than 26 years.

c) There is not enough information to perform the test.

d) Do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 24.4 years.

e) Reject the null hypothesis. There is sufficient evidence that the mean age is less than 24.4 years.

State your conclusion to the hypothesis test.

4.A certain academic program claims that their students graduate in less than 4 years on average. A random sample of 50 students is taken and the mean and standard deviation are found. The test statistic is calculated to be -1.69. Using a 5% significance level, the conclusion would be:

a) there is sufficient sample evidence for the program's claim to be considered correct.

b) there is insufficient sample evidence for the program's claim to be considered correct.

c) there is insufficient sample evidence for the program's claim to be considered incorrect.

d) there is sufficient sample evidence for the program's claim to be considered incorrect.

State your conclusion to the hypothesis test.

5.A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 22 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of n=33 wind speed recordings (taken at random intervals), the wind speed at the site averaged 22.8 mph, with a standard deviation of 4.3 mph. To determine whether the site meets the organization's requirements, perform the following hypothesis test at the 1% significance level and state your conclusion.

Ho: μ = 22

HA: μ > 22

a) At α = .01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 22 mph.

b) At α = .01, there is not sufficient evidence to conclude the true mean wind speed at the site exceeds 22 mph.

c) We are 99% confident that the site meets the organization's requirements.

d) We are 99% confident that the site does not meet the organization's requirements.

Assume a normal distribution and use a hypothesis test to test the given claim.

6.A firework fuse is designed to have an average burn-time of 5 seconds before ignition. For liability reasons, the company that makes these fuses undergoes random testing to make sure that its fuses meet this standard. A random sample of 20 fuses results in an average burn-time of 5.3 seconds with a sample standard deviation of 0.7 seconds.

Assuming the burn-time for an individual fuse is normally distributed, perform the appropriate hypothesis test at a 5% significance level to determine if the fuses perform according to design.

a) There is insufficient evidence to conclude the burn time is not 5 seconds.

b) There is sufficient evidence to conclude the burn time is greater than 5 seconds.

c) There is sufficient evidence to conclude the burn time is less than 5 seconds.

d) There is sufficient evidence to conclude the burn time is not 5 seconds.

e) There is insufficient evidence to conclude the burn time is 5 seconds.

Select the most appropriate response.

7.The level of significance, alpha, for a test of hypothesis represents:

a) the probability that the test statistic will fall in the rejection region, assuming the null hypothesis is true.

b) the acceptable probability of making a Type I error.

c) the probability of rejecting the null hypothesis when it is in fact true.

d) all of the above.

State your conclusion to the hypothesis test.

8.If a 95% confidence interval for μ is calculated to be (21.4 , 27.9) , what would be the result of a hypothesis test at a 5% significance level performed on the set of hypotheses?  

H0 : μ = 27 vs H1 : μ ≠ 27

a) There is not enough information to test this hypothesis.

b) The null hypothesis would be rejected.

c) The alternative hypothesis would be rejected.

d) The null hypothesis would not be rejected.