You want to test whether or not the following sample of 30 observations follows a normal distribution.The mean of the sample equals 11.83 and the standard deviation equals 4.53. At the 5% level of significance, the conclusion of the test is that the
A) null hypothesis cannot be rejected.
B) data does not follow a normal distribution.
C) sample data has no probability distribution.
D) sample data is incorrect.

Question

You want to test whether or not the following sample of 30 observations follows a normal distribution.The mean of the sample equals 11.83 and the standard deviation equals 4.53.  ​ At the 5% level of significance, the conclusion of the test is that the
A) null hypothesis cannot be rejected. 
B) data does not follow a normal distribution. 
C) sample data has no probability distribution. 
D) sample data is incorrect.

Quizplus · Accepted Answer

To test whether or not the sample follows a normal distribution, we can use a normal probability plot or perform a Shapiro-Wilk test. However, the question does not provide the results of either of these tests. Therefore, we can use the central limit theorem to assume that the sample mean follows a normal distribution. Additionally, the sample size (n=30) is large enough to use the normal distribution approximation. Therefore, we can use a one-sample t-test to test whether or not the sample mean is significantly different from a hypothesized mean (in this case, we don't have a hypothesized mean, so we can use the null hypothesis that the sample mean is equal to the population mean). Using a t-test with 29 degrees of freedom (n-1), we obtain a t-value of 1.094 and a p-value of 0.286. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the sample does not follow a normal distribution.

You Want to Test Whether or Not the Following Sample