Exam 10: Hypothesis Tests Based on a Single Sample

For a hypothesis test, the smallest significance level for which the null hypothesis can be rejected is the:

Suppose you reject the null hypothesis at the α = 0.05 significance level.Would you reject it at the α = 0.01 level?

If the decision from a hypothesis test is to fail to reject the null hypothesis when in reality the null hypothesis is false, the test has:

A test of hypothesis has the following details: ​ H₀: μ = 28, Ha: μ < 28, n = 40, σ = 6.6, α = 0.10 ​ Calculate β if the population mean is 27.5.

Psychologists wish to evaluate the consistency of a standardized behavioral test.The test is designed to have a variance of 225.Twenty randomly sampled tests yield a variance of 240.Assuming the underlying population is normal, test whether the actual population variance of this test appears to be significantly greater than its designed variance.State the critical value (CV), test statistic (TS), and conclusion from the test.(Use α = 0.01.)

A two-tailed test of hypothesis has a p-value = 0.0055.The critical value from the test is 0.9800.The type I error probability for the test is 0.01.What is the correct decision for the test and why is this reason correct?

If the decision from a hypothesis test is to reject the null hypothesis when in reality the null hypothesis is false, the test has:

In the trucking industry, nights away from home are an unfortunate reality of this profession.Big shipping companies attempt to lure potential drivers by promising more time at home.One such company claims that its drivers spend 98% of their evenings at home.A random sample of truckers from the company reveals that out of a total of 3514 days, 3405 evenings were spent at home.Based on the sample, does it appear that the claim is too high? State the critical value (CV), test statistic (TS), and decision from the test.(Use α = 0.05.)

Previous research indicates that 20% of homeowners do not carry sufficient homeowner's insurance to adequately protect their investment.An insurance agency conducts a major advertising campaign in an attempt to rectify this situation.After the campaign, the agency randomly surveys 150 homeowners and find that 20 of them do not carry sufficient insurance.Does it appear that the proportion of homeowners without sufficient insurance was less after the ad campaign? State the critical value (CV), test statistic (TS), and decision from the test.(Use α = 0.05.)

An associate at a large home improvement store claims that she can build a composite 12 × 20 ft deck for an average cost of $7200.We sample eight decks built by this associate and find that the average cost was $8215.22 with a standard deviation of $711.16.Does it appear from this sample that the claim of $7200 is not accurate (either too high or too low)? State the critical value (CV), test statistic (TS), and decision from the test.(Use α = 0.05.)

In a study of parents' perceptions of their children's size, researchers asked parents to estimate their youngest child's height.The researchers hypothesize that parents tend to underestimate their youngest child's size because the youngest child is the baby of the family and all other family members appear larger compared to the baby.The sample of 39 parents who were surveyed underestimated their youngest child's height by 7.5 cm, on average; the standard deviation for the difference in actual heights and estimated heights was 7.2 cm, and the data were approximately normal.Determine the TS and p-value for this study.

For any hypothesis test, the amount of evidence required to overturn (reject) the null hypothesis can be expressed by:

Which of the following statements is true regarding a hypothesis test on variance that uses the chi-square distribution?

Suppose that a Z-score for a study is calculated to be 2.45.Which of the following is the most appropriate interpretation of this z-score?

Patrons at a local batting cage complain that a pitching machine set to throw 80 mph is throwing too slowly.A random sample of 29 pitches from the machine yields an average speed of 79.25 mph with a standard deviation of 4.22 mph.Perform a hypothesis test to see if the average speed of this machine is less than 80 mph.Select the appropriate critical value (CV), test statistic (TS), and decision, and list H₀.(Use α = 0.01.)

In September 2000, St.George's Hospital in London was suspended from performing heart transplants because of a sudden spike in the mortality rate.Researchers recorded information from a sample of 361 patients and used this to test whether the mortality rate at St.George's Hospital was greater than the national rate of 15%.What would a type II error be in this situation?

Suppose we decide to raise the probability of a type I error.What effect (if any) will raising the type I error probability have on β?

A shoe salesman wishes to check the validity of his supplier's claim that the average length of the adult male foot is 9.34 in.He randomly samples 35 adult male customers and finds their average foot length to be 9.01 in.The standard deviation of foot length is known to be 0.75 in.What would be the appropriate alternative hypothesis if the salesman thinks the supplier's claim is too high?

An intern is working on survey data for a political candidate who wishes to statistically disprove a claim his opponent made.Halfway through the analysis, the intern changes from a "not equal" to a "greater than" alternative hypothesis.What effect does this have on the results?

When we get a p-value that is very large, we may conclude that: