1. The test statistic value gives a Type I error for a significance level of 5% and a correct decision for a significance level of 2% is 1.64.
2. If the researcher had used a significance level of 1% then the p-value decreases.
3. Among the given options, (d) The test statistic is -1.77, and the true mean is 84 could be true, as it suggests a less extreme value for a lower true mean.
4. Looking at the given p-values, 0.065, 0.045, and 0.025 might have occurred, as they all represent non-rejection regions.
5. The possible values for the test statistic include (c) 0.85 and (d) 1.88.
6. The correct answer (c) We have a Type II error if the null hypothesis is true.
1. To determine the test statistic value that gives a Type I error for a significance level of 5% and a correct decision for a significance level of 2%, we need the critical values for both scenarios.
Using a standard normal distribution table, the critical values for a 5% significance level are approximately ±1.96, and for a 2% significance level, they are approximately ±2.33.
Therefore, the correct answer is (b) 1.64.
2. If the researcher had used a significance level of 1%, the critical value would be more extreme than at 5%.
This would result in a smaller acceptance region and, consequently, a smaller p-value.
Therefore, the correct answer is (c) the p-value decreases.
3. A Type II error occurs when the null hypothesis is not rejected when it is false.
This means the test statistic is not extreme enough.
Among the given options, (d) The test statistic is -1.77, and the true mean is 84 could be true, as it suggests a less extreme value for a lower true mean.
4. For a Type II error at a significance level of 4%, the researcher fails to reject a false null hypothesis. Looking at the given p-values, 0.065, 0.045, and 0.025 might have occurred, as they all represent non-rejection regions.
5. For a two-tailed test with a false null hypothesis, the critical values would be approximately ±2.09 at a 5% significance level with a sample size of 20.
Therefore, possible values for the test statistic include (c) 0.85 and (d) 1.88.
6. With a right-tailed test, the critical value for a 5% significance level is approximately 1.645. Since the test statistic is 1.48, we fail to reject the null hypothesis.
This leads to a Type II error if the null hypothesis is false, making the correct answer (c) We have a Type II error if the null hypothesis is true.
The probable question may be:
1. We have a right tail test for a population mean. The sample size is 32. Assume the null hypothesis is true. Which test statistic value gives a Type I error for a significance level of 5% and a correct decision for a significance level of 2%? (a) 1.34 (b) 1.64 (c) 1.94 (d) 2.24
2. A researcher performs a right-tailed hypothesis test for the mean of a certain population. The researcher used a significance level of 5%. If the researcher had used a significance level of 1% then (a) the p-value remains the same (b) the p-value increases (c) the p-value decreases (d) the effect on the p-value is unknown.
3. A Type Il error occurred. The alternative hypothesis is the mean is less than 80. The sample size is 22 and the significance level is 5%. Which of the following could be true? (a) the test statistic is -1.47 and the true mean is 76. (b) The test statistic is -1.77 and the true mean is 76 (c) The test statistic is -1.47 and the true mean is 84. (d) The test statistic is -1.77 and the true mean is 84.
4. This is a fill in the blank question. A hypothesis test had a Type Il error using a significance level of 4%. Listed below are several p-values. Write down on the answer sheet all p-values that might have occurred. 0.085,0.065,0.045,0.025,0.015,0.005
5. We have a correct decision for a two-tailed hypothesis test. The null hypothesis is false. The significance level is 5%, and the sample size is 20. Which of these are possible values for the test statistic?
(a) -2.24 (b) -2.04 (c) 0.85 (d) 1.88
6. We have a right-tailed test. The test statistic is 1.48, the sample size is 28 and the significance level is 5%. Find out if the null hypothesis is rejected. Based on that result, which of the following is true?
(a) We have a Type I error if the null hypothesis is true.
(b) We have a Type I error if the null hypothesis is false.
(c) We have a Type Il error if the null hypothesis is true.
(d) We have a Type Il error if the null hypothesis is false.