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. $$\begin{array} { l l l l l l l l l l }
2 & 3 & 5 & 5 & 7 & 8 & 8 & 9 & 9 & 10 \
11 & 11 & 12 & 12 & 12 & 12 & 13 & 13 & 13 & 14 \
15 & 15 & 15 & 16 & 16 & 17 & 17 & 18 & 18 & 19
\end{array}$$ 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. $$\begin{array} { l l l l l l l l l l } 
2 & 3 & 5 & 5 & 7 & 8 & 8 & 9 & 9 & 10 \
11 & 11 & 12 & 12 & 12 & 12 & 13 & 13 & 13 & 14 \
15 & 15 & 15 & 16 & 16 & 17 & 17 & 18 & 18 & 19
\end{array}$$   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

The sample size is 30, which is sufficient to use the Shapiro-Wilk test or similar tests for normality. Given the sample mean and standard deviation, the data does not show significant deviation from normality at the 5% significance level, so the null hypothesis of normality cannot be rejected.

You Want to Test Whether or Not the Following Sample