FiltersDone

Question type

Essay

Multiple Choice

Short Answer

True False

Matching

Exam 13: Hypothesis Testing: Describing a Single Population

Show Answer

Share

---

All types

Filters

Study FlashcardsPractice ExamLearn

Question 61

Essay

Review LaterAdd Note

Review Later

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?

Correct Answer

verified

. .
Rejection region: |z| > ...

View Answer

Show Answer

Question 62

Essay

Review LaterAdd Note

Review Later

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

Correct Answer

verified

a. Appropriate, because the population p...

View Answer

Show Answer

Question 63

True/False

Review LaterAdd Note

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

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

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:

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).

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.

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 10 observations are drawn from a normal population whose variance is 64. The observations are: $\begin{array} { | r | r | r | r | r | r | r | r | r | r | } \hline 13 & 21 & 15 & 19 & 35 & 24 & 14 & 18 & 27 & 30 \\\hline\end{array}$ Test at the 10% level of significance to determine whether there is enough evidence to conclude that the population mean is greater than 20.

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?

The power of a test is the probability of making:

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

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

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

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.

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

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?