In testing the null hypothesis Ho: μ = 75 against the alternative Ha: μ > 75, a sample from a normal population has a mean of 76.9 with a corresponding t-score of 2.23 and a P-value of .0175. Which of the following is not a reasonable conclusion?

• If the null hypothesis is assumed to be true, the probability of obtaining a sample mean as extreme as or more extreme than 76.9 is only .0175

• In all samples using the same sample size and the same sampling technique, the null hypothesis will be wrong 1.75% of the time.

• At α = 0.05, there is sufficient evidence to reject the null hypothesis

• If the population standard deviation σ had been known, then the z-score of 2.23 would have resulted in a smaller P-value.

• If the alternative hypothesis had been two-sided, then the same t-score would have resulted in a P-value of 2 x .0175

If all other variables remain constant, which of the following will not increase the power of a hypothesis test?

• Increasing the sample size

• Increasing the significance level

• Increasing the probability of a Type II error

• Decreased variability in the sample data

• Increased distance between the true and hypothesized parameter

Two pain relief medicines are tested on volunteer post-operation patients, randomly assigned to one of the two brands of medicine, as to whether or not mean duration of relief are different. Data is recorded in minutes of pain relief. What is the conclusion of the appropriate hypothesis test for this experiment?

• P < .05 so reject Ho

• P < .05 so fail to reject Ho

• P > .05 so reject Ho

• P > .05 so fail to reject Ho

• 5% significance level is inappropriate for medical decisions

An HR executive wishes to know the difference in job satisfaction rating (on a standard satisfaction test) between employees who exercise regularly and those who don't. The standard deviation for this satisfaction test is known to be 4.5 for each group. Suppose the HR executive will take a random sample of the same size from each population of employee to be interviewed. What should this sample size be if the executive wishes to be 90% confident of knowing the difference in rating to within 1 point?

• 10

• 55

• 110

• 156

• 202

Tags

CCSS.HSS.IC.B.4

Given that the power of a significance test against a particular alternative is 96%, which of the following is true?

• The probability of mistakenly rejecting a true null hypothesis is less than 4%

• The probability of mistakenly rejecting a true null hypothesis is 4%

• The probability of mistakenly rejecting a true null hypothesis is greater than 4%

• The probability of mistakenly failing to reject a false null hypothesis is 4%

• The probability of mistakenly failing to reject a false null hypothesis is different from 4%

Tags

CCSS.HSS.MD.A.2

A company that produces paper towels continually monitors wet towel strength. If the mean strength from a sample drops below a specified level, the production process is halted, and the machinery inspected. Which of the following would result form a Type 1 error?

• Halting the production process when sufficient customer complaints are received

• Halting the production process when the wet towel strength is below specifications

• Halting the production process when the wet towel strength is within specifications

• Allowing the production process to continue when the wet towel strength is below specifications

• Allowing the production process to continue when the wet towel strength is within specifications

Two students use the same data to perform significance tests. One student performs a test Ho: p = .85 vs Ha: p ≠ .85, the other student performs a test Ho: p = .85 vs Ha: p < .85. Even though they both use α = .05, the first student claims there is not enough evidence to reject Ho, and the second student claims there is enough evidence to reject Ho. Which of the following could have been the value for the test statistic?

• z = -2.3

• z = -1.8

• z = -1.3

• z = 1.8

• Any of these could have been the test statistic.

In a comparison of the life expectancy of two models of washing machines, the average years before breakdown in an SRS of 10 machines of one model is compared to that of 15 machines of a second model. The 95% confidence interval estimate of the difference is (6, 12). Which of the following is the most reasonable conclusion?

• The mean life expectancy of one model is twice that of the other

• The mean life expectancy of one model is 6 years, while the mean life expectancy of the other is 12 years

• The probability the life expectancies are different .95

• The probability the difference in life expectancies is greater than 6 is .95

• We should be 95% confident that the difference in life expectancies is between 6 and 12 years

Tags

CCSS.HSS.IC.B.4

Changing from a 95% confidence interval estimate for a difference in population proportions to a 99% confidence interval estimate, with all other things being equal, ...

• increases the interval size by 4%

• decreases the interval size by 4%

• increases the interval size by 31%

• decreases the interval size by 31%

• This question cannot be answered without knowing the sample sizes

A real-estate investor wishes to estimate the difference in the average house price in San Diego to that of Miami, a random sample of 100 homes are taken from each city. Which of the following is most appropriate?

• A two-sample z interval

• A two-sample z test

• A two-sample t interval

• A matched-pairs t interval

• None of the above are appropriate

Tags

CCSS.HSS.IC.B.4