The heights (in cm) for a random sample of 60 males were measured. The sample mean is 166.55, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. The following table shows the heights subdivided into non-overlapping intervals. Suppose the value of the test statistic is 7.71. Using the critical value approach, decision and conclusion are ________.
A) reject the null hypothesis; conclude that heights are normally distributed
B) reject the null hypothesis; conclude that heights are not normally distributed
C) do not reject the null hypothesis; conclude that heights are normally distributed
D) do not reject the null hypothesis; conclude that heights are not normally distributed

Question

The heights (in cm) for a random sample of 60 males were measured. The sample mean is 166.55, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. The following table shows the heights subdivided into non-overlapping intervals.  Suppose the value of the test statistic is 7.71. Using the critical value approach, decision and conclusion are ________.
A) reject the null hypothesis; conclude that heights are normally distributed 
B) reject the null hypothesis; conclude that heights are not normally distributed 
C) do not reject the null hypothesis; conclude that heights are normally distributed 
D) do not reject the null hypothesis; conclude that heights are not normally distributed

Quizplus · Accepted Answer

The null hypothesis is that the heights are normally distributed. The test statistic is calculated using the sample mean, standard deviation, skewness, and kurtosis. If the test statistic is larger than the critical value, we reject the null hypothesis, which means that the heights are not normally distributed.

Using the critical value approach, we look up the critical value for the given significance level and degrees of freedom (n-1), and compare it to the test statistic. If the test statistic is larger than the critical value, we reject the null hypothesis.

Since the question does not provide the significance level or degrees of freedom, we cannot determine the exact critical value. However, we can conclude that the test statistic of 7.71 is very large, and it is likely to exceed the critical value for any reasonable significance level. Therefore, we reject the null hypothesis and conclude that the heights are not normally distributed (choice B).

The Heights (In Cm) for a Random Sample of 60