Exam 12: Hypothesis Testing: Describing a Single Population

In testing the hypotheses: H0: μ = 40 HA: μ  40 the following information was given:  = 5.5, n = 25, $\bar { X }$ = 42, α = 0.10, and the sampled population is normally distributed. a. Calculate the value of the test statistic. b. Set up the rejection region. c. Determine the p-value. d. Interpret the result.

In testing the hypotheses: H0: μ = 950 HA: μ  950 the following information was given: μ = 1000,  = 0.05, σ = 180 and n = 75. Determine β.

In a criminal trial, a Type I error is made when:

Consider the hypotheses H0: μ = 950 HA: μ  950 Assume that μ = 1000,  = 200, n = 25,  = 0.10 and  = 0.6535. When we recalculate  if $\alpha$ is lowered from 0.10 to 0.05, β = 0.7604. What is the effect of decreasing the significance level on the value of?

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)?

Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.10?

Consider the hypotheses H0: μ = 950 HA: μ  950 Assume that μ = 1000,  = 200, n = 25,  = 0.10 and  = 0.6535. When we recalculate $\beta$ if n is increased from 25 to 40,  = 0.5233. What is the effect of increasing the sample size n on the value of  and the power of the test?

The probability of a Type I error is denoted by:

In testing the hypotheses: H0: μ = 25 HA: μ  25 a random sample of 36 observations drawn from a normal population whose standard deviation is 10 produced a mean of 22.8. Compute the p-value.

The p-value criterion for hypothesis testing is to retain the null hypothesis if:

Statisticians can translate p-values into several descriptive terms. Which of the following statements is correct?

In a criminal trial, a Type II error is made when an innocent person is acquitted.

If the p-value for a one tail test is 0.03, would you have the same conclusion at a significance level of 0.05 and at a significance level of 0.10?

When testing whether the majority of voters in an electorate will vote for a particular candidate, which of the following sets of hypotheses are correct?

In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is true, a Type I error is committed.

In testing the hypotheses: H0: μ = 950 HA: μ  950 the following information was given: μ = 1000,  = 0.05, σ = 180 and n = 75. It was found that β = 0.3264. a. Recalculate β if n = 100. b. What is the effect of increasing the sample size on the value of β?

In testing the hypotheses H0: μ = 24.4 HA: μ > 24.4 the following information was given:  = 7.6, n = 60, $\bar { X }$ = 25.52,  = 0.06. a. Calculate the value of the test statistic. b. Set up the rejection region. c. Determine the p-value. d. Interpret the result.

In testing the hypotheses: H0: μ = 25 HA: μ  25 a random sample of 36 observations was drawn from a normal population. The sample standard deviation is 10 and the sample mean is 22.8. Can we conclude at the 5% significance level that the population mean is not significantly different to 25?

Formulate the null and alternative hypotheses for each of the following statements: a. The average Australian household owns 2.5 cars. b. A researcher at the University of Adelaide is looking for evidence to conclude that the majority of students drive to university. c. The manager of the University of Tasmania bookstore claims that the average student spends less than $400 per semester at the university's bookstore.

Which of the following test statistics may be used to test a value of the population proportion?