Exam 13: Hypothesis Testing: Describing a Single Population

At present, many universities in Australia are adopting the practice of having lecture recordings automatically available to students. A university lecturer is trying to investigate whether having lecture recordings available to students has significantly decreased the proportion of students passing her course. When lecture recordings were not provided to students, the proportion of students that passed her course was 80%. The lecturer takes a random sample of 25 students, when lecture recordings are offered to students, and finds that 11 students have passed the course. Is there significant evidence to support this university lecturer's claim? Use the p-value method and test at α = 0.01

If a hypothesis is not rejected at the 0.10 level of significance, it: A. must be rejected at the 0.05 level. B. may be rejected at the 0.05 level. C. will not be rejected at the 0.05 level. D. must be rejected at the 0.025 level.

The confidence interval approach can be employed to conduct tests of hypotheses. Which of the following statements is false? A. The confidence interval approach is equivalent to the rejection region approach. B. The confidence interval approach has the disadvantage of complexity. C. One-sided confidence intervals can be used when conducting a one-tail test. D. The confidence interval approach does not yield a p -value.

A null hypothesis is a statement about the value of a population parameter; it is put up for testing in the face of numerical evidence.

In testing the hypotheses: H₀ : $\mu$ = 22. H₁ : $\mu$ < 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.

If we do not reject the null hypothesis, we conclude that: A there is enough statistical evidence to infer that the alternative hypothesis is true. B there is not enough statistical evidence to infer that the al ternative hypothesis is true. C there is enough statistical evidence to infer that the null hypothesis is true. D the test is statistically insignificant at whatever level of significance the test was conducted at.

In testing the hypotheses: $H _ { 0 } : \mu = 25$ $H _ { 1 } : \mu \neq 25$ , a random sample of 36 observations drawn from a normal population whose standard deviation is 10 produced a mean of 22.8. Explain briefly how to use the confidence interval in the previous question to test the hypothesis.

A Type II error is committed if we make: A. a correct decision when the null hypothesis is false. B. correct decision when the null hypothesis is true. C. incorrect decision when the null hypothesis is false. D. incorrect decision when the null hypothesis is true.

Suppose that 10 observations are drawn from a normal population whose variance is 64. The observations are: 13 21 15 19 35 24 14 18 27 30 Test at the 10% level of significance to determine whether there is enough evidence to conclude that the population mean is greater than 20.

In any test, the probability of a Type I error and the probability of a Type II error add up to 1.

For each of the following statements, state the population parameter of interest, state the appropriate null and alternative hypotheses and indicate whether the appropriate test will be a two-tailed, a left tailed or a right tailed test. a. The average age a person registers to vote in Australia is greater than 20 years. b. A minority of office workers purchase their morning coffee. c. The average number of hours spent on a computer per day. d. The majority of students in a particular university course who attend lectures has changed from 75%, since lecture recordings have become freely available to students.

In a criminal trial, a Type I error is made when an innocent person is convicted.

A Type I error is represented by $\beta$ , and is the probability of not rejecting a false null hypothesis.

The power of a test is the probability of making: A. a correct decision when the null hypothesis is false. B. a correct decision when the null hypothesis is true. C. an incorrect decision when the null hypothesis is false. D. an incorrect decision when the null hypothesis is true.

In testing the hypotheses: $H _ { 0 } : \mu = 25$ $H _ { 1 } : \mu \neq 25$ , 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?

If a null hypothesis is rejected at the 0.05 level of significance, it cannot be rejected at the 0.10 level.

There is a direct relationship between the power of a test and the probability of a Type II error.

The power of a test is the probability that it will lead us to: A. reject the null hypothesis when it is true. B. reject the null hypothesis when it is false. C. fail to reject the null hypothesis when it is true. D. fail to reject the null hypothesis when it is false.

Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.10? A. 0.001. B. 0.01 C. 0.05 D. All of these choices are correct.

The rejection region for testing the hypotheses $H _ { 0 } : \mu =$ 100. $H _ { 1 } : \mu \neq$ 100. at the 0.05 level of significance is: A. |z|<0.95. B. z\mid>1.96. C. z>1.65. D. z<2.33.