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

To determine whether the heights are normally distributed or not, we need to perform a normality test. One of the commonly used tests is the Shapiro-Wilk test. However, the problem does not give the p-value of the test. Instead, it gives us the test statistic (7.71), which we can use to compare against the critical value.

Assuming a significance level of 0.05, the critical value for a normality test with 60 samples is 0.873. If the test statistic is greater than the critical value, we reject the null hypothesis of normality. If it is less than or equal to the critical value, we fail to reject the null hypothesis.

In this case, the test statistic (7.71) is much larger than the critical value (0.873), indicating a significant departure from normality. Therefore, we reject the null hypothesis and conclude that heights are not normally distributed.

Note that the sample kurtosis and skewness are not reliable indicators of normality, especially with small sample sizes like ours. Hence, the formal normality test is necessary.

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