Exam 13: Hypothesis Testing: Describing a Single Population

Consider the hypotheses $H_ { 0 } : \mu = 950$ $H _ { 1 } : \mu \neq 950$ . Assume that $\mu = 1000$ $\alpha = 0.10$ $\sigma = 200$ , and n = 25. Calculate $\beta$ , the probability of a Type II error.

A random sample of 100 families in a large city revealed that on the average these families have been living in their current homes for 35 months. From previous analyses, we know that the population standard deviation is 30 months. Can we conclude at the 5% significance level that the true mean number of months families in this city have been living in their current homes is at least 30 months?

A two-tail test is a test in which a null hypothesis can be rejected by an extreme result occurring in either direction.

Which of the following best describes the p-value of a test?

In testing the hypotheses: H₀ : ? = 950 H₁ : ? $\neq$$\neq$ 950, the following information was given: ? = 1000, $\alpha$ = 0.05, ? = 180 and n = 75. Determine ?.

Given that s = 15, n = 50, x-bar = 17.5, $\alpha$ = 0.05, test the following hypotheses: H₀ : ? = 22. H₁ : ? ? 22

The critical values z $\alpha$ or z $\alpha$ / 2 are the boundary values for the:

In our justice system, judges instruct juries to find the defendant guilty only if there is evidence 'beyond a reasonable doubt'. In general, what would be the result if judges instructed juries: a. to compromise between Type I and Type II errors? b. never to commit a Type I error? c. never to commit a Type II error?

Consider the hypotheses $H_ { 0 } : \mu = 950$ $H _ { 1 } : \mu \neq 950$ . Assume that $\mu = 1000$ $\alpha = 0.10$ $\sigma = 200$ , and n = 25 and $\beta$ = 0.6535 when we recalculate $\beta$ if n is increased from 25 to 4, β = 0.5233. What is the effect of increasing the sample size on the value of $\beta$ ?

Which of the following statements is (are) not true?

The p-value of a test is the smallest value of $\alpha$ at which the null hypothesis can be rejected.

In a one-tail test, the p-value is found to be equal to 0.032. If the test had been two-tailed, the p-value would have been:

In testing the hypotheses: H₀ : ? = 22. H₁ : ? < 22 the following information was given: $\sigma$ = 15, n = 50, x-bar = 17.5, $\alpha$ = 0.04. a. Calculate the value of the test statistic. b. Set up the rejection region. c. Determine the p-value. d. Interpret the result.

In order to determine the p-value, which of the following items of information is not needed?

A Type I error is committed if we make:

The power of a test is denoted by:

When using a t-test to test the population mean, the degrees of freedom are n - 1.

The admissions officer for the graduate programs at the University of Adelaide believes that the average score on an exam at his university is significantly higher than the national average of 1300. Assume that the population standard deviation is 125 and that a random sample of 25 scores had an average of 1375. a. State the appropriate null and alternative hypotheses. b. Calculate the value of the test statistic and set up the rejection region. What is your conclusion? c. Calculate the p-value. d. Does the p-value confirm the conclusion in part (b)?

A Type I error is represented by $\alpha$ , and is the probability of rejecting a true null hypothesis.

A drug company is interested in the effectiveness of a new sleeping pill. A random sample of 50 people try the new sleeping pill and the number of additional hours of sleep (compared with the nights without any sleeping pill), X, are recorded. The sample standard deviation of X is 3 hours. a. State the null and alternative hypotheses for the claim that the new drug increases the number of hours of sleep at least by 2 hours on average. b. Using a standardised test statistic, test the hypothesis at the 5% level of significance if the sample mean of additional hours of sleep is 2.2 hours.