State whether the following statements are True or False 5 m

State whether the following statements are True or False. (5 marks, 1 Mark Each)

  A Type II error is rejecting a true null hypothesis.

When testing a null hypothesis about a single population mean and the population standard deviation is unknown, if the sample size is less than 30, one compares the computed test statistic for significance with a value from the Z- distribution.

  As the level of significance a decreases, we are more likely to fail to reject the null hypothesis.

For a hypothesis test about a population proportion or mean, if the level of significance is greater than the p-value, fail to reject null the null hypothesis.                                               

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the variances are pooled to compute the best estimated variance.

Section-II

(Multiple Choice Questions)                                (5 marks, 1 Mark Each)

1. Which of the following is not one of the steps for hypothesis testing?

A. Determine the null and alternative hypotheses.

B. Verify data conditions and calculate a test statistic.

C. Assuming the null hypothesis is true, find the p-value.

D. Assuming the alternative hypothesis is true, find the p-value.

2. The p-value for a one-sided test for a mean was 0.06. The p-value for the corresponding two-sided test would be:

A. 0.12

B. 0.04

C. 0.06

D. 0.08

3. Which statement is incorrect?

A. The null hypothesis contains the equality sign.

B. When a false null hypothesis is not rejected, a Type II error has occurred.

C. If the null hypothesis is rejected, it is concluded that the alternative hypothesis is true.

D. If we fail to reject the null hypothesis, then it is proven that null hypothesis is true.

4. The null and alternative hypotheses divide all possibilities into:

         A. Two sets that overlap

B. Two non-overlapping sets

C. Two sets that may or may not overlap

D. As many sets as necessary to cover all possibilities

   5. When testing for the equality of two population means, using = 0.05 with n₁ = 12 and n₂ = 10, from independent samples, so long as the population variances can be assumed equal, the critical values for t are:

         A) +2.704 and -2.704

         B) +1.96 and -1.96

         C) +2.086 and -2.086

         D) +1.645 and -1.645

         E) None of the above

Solution

1. A Type II error is rejecting a true null hypothesis. [TRUE, ANSWER]

****************

2. When testing a null hypothesis about a single population mean and the population standard deviation is unknown, if the sample size is less than 30, one compares the computed test statistic for significance with a value from the Z- distribution.   

[FALSE, we should use the T distirbution when n < 30.]

*******************

3.

As the level of significance a decreases, we are more likely to fail to reject the null hypothesis.

FALSE. It makes it more likely. [ANSWER]

*****************

4.
For a hypothesis test about a population proportion or mean, if the level of significance is greater than the p-value, fail to reject null the null hypothesis.
FALSE. We reject Ho if alpah > P or P < alpha.

**********************
5.
  
If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the variances are pooled to compute the best estimated variance.

TRUE. [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!