Exam 13: Hypothesis Testing: Describing a Single Population

In testing the hypotheses: $H _ { 0 } : \mu =$ 35 H₁ : $\mu$ < 35, The following information is known: n = 49, $\bar { x }$ = 37 and $\sigma$ = 16. The standardised test statistic equals:

In testing the hypotheses $H _ { 0 } : \mu =$ 75. $H _ { 1 } :$ $\mu$ < 75. if the value of the Z test statistic equals 1.78, then the p-value is:

In order to determine the p-value, it is not necessary to know the level of significance.

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, and that ? = 0.2061. a. Calculate the power of the test. b. Interpret your answer to part (a).

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.

A random sample of 100 observations from a normal population whose standard deviation is 50 produced a mean of 75. Does this statistic provide sufficient evidence at the 5% level of significance to infer that the population mean is not 80?

The critical values will bound the rejection and non-rejection regions for the null hypothesis.

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

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

State which of the following set of hypotheses are appropriate. Explain a. Ho: µ = 25 H₁: µ ≠ 25 b. Ho: µ > 25 H₁: µ = 25 c. $H _ { 0 } :$ $\bar { x } = 35$ . $H _ { 1 } : \bar { x } > 35$ . d. Ho: p = 25 H₁: p ≠ 25 e. Ho: p = 0.5 H₁: p > 0.5

The power of a test is the probability that it will lead us to:

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 and the power of the test is 0.3465 Interpret the meaning of the power in the previous question.

In testing the hypotheses: $H _ { 0 } : \mu = 25$ $H _ { 1 } : \mu \neq 25$ , a random sample of 36 observations drawn from a normal population, produced a mean of 22.8 and a standard deviation of 10 What is the conclusion for this hypothesis test, at 5% significance level.

The rejection region for testing the hypotheses $H _ { 0 } : \mu =$ 100. $H _ { 1 } : \mu \neq$ 100. at the 0.05 level of significance is:

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.

The power of a test is the probability of making:

Determine the p-value associated with each of the following values of the standardised test statistic z. a. Two-tail test, z = 1.50. b. One-tail test, z = 1.05. c. One-tail test, z = -2.40.

Suppose that we reject a null hypothesis at the 0.05 level of significance. For which of the following $\alpha$ -values do we also reject the null hypothesis?

There is an inverse relationship between the probabilities of Type I and Type II errors.

A Type II error is represented by $\beta$ and is the probability of failing to reject a false null hypothesis.