Question

(Questions 1 and 2) An experiment is conducted. The sample size is 30. A sample average is observed. To test the null hypothesis that the population average equals a particular value versus the alternative hypothesis that the population average is not equal to a particular value, a two tailed hypothesis test is performed. (Critical region in the two tails). The test statistic— the sample average—is normally distributed. The stated significance levels for the test are 5% and 1%. In other words, the null hypothesis is rejected at a stated significance level of 5% or 1%.

1. (Use the z table to answer this question) Suppose the observed value of the Z statistic is -2.10. The researcher should

1. Reject the null hypothesis at the 5% level of significance but not the 1% level of significance
2. Reject the null hypothesis at the 1% level of significance
3. Do not reject the null hypothesis at the 5% level of significance
4. Because the sample size is too small, increase the sample size before performing the test to lower the standard error
5. None of the above

2. (Use the z table to answer this question) If the observed value of the z statistic is -2.10, the observed significance level, (the p value) is:

1. 5%
2. 2.5%
3. 1.785%
4. 2.10%
5. None of the above

(Question 3) A researcher wishes to test the null hypothesis that a die is fair against the alternative hypotheses that a die is not fair. A die is rolled 360 times. There are 6 categories. The observed value of the chi square statistic is 10.23.

3. (Use the chi square table to answer this question) In her written report of the results of the experiment, the researcher should declare,

1. The result is significant at the 1% level, that is, the result is highly significant.
2. The result is significant at the 5% level but not the 1% level, that is, the result is statistically significant.
3. The result is not significant at the either the 1% level or the 5% level.
4. The degrees of freedom are insufficient to perform the test.
5. None of the above

Answer 1

1) Answer: Reject the null hypothesis at the 5% level of significance but not the 1% level of significance

Explanation:

The critical value at 5% level of significance = -1.96

The critical value at 1% level of significance = -2.58

The observed value of z statistic is less than-1.96 but greater than -2.58. Hence we reject the null hypothesis at the 5% level of significance but not the 1% level of significance

2) Answer: None of these

Explanation:

P-value = 2*P(Z < -2.10)

             =2*(0.0179)

P-value =0.0358

P-value = 3.58%

3) Answer: The result is not significant at the either the 1% level or the 5% level.

Explanation:

The degrees of freedom for Chi-square test = k-1 = 6-1=5

The critical value of chi-square at 5 df and 5% level of significance = 11.07

The critical value of chi-square at 5 df and 1% level of significance = 15.09

The value of chi square statistic is less than both critical values. Hence we conclude that the result is not significant at the either the 1% level or the 5% level.