Suppose that a random sample of 150 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardized and the number of observations in each of the intervals below was counted. Can we infer at the 5% significance level that the data were drawn from a normal population?
$\begin{array} { | l | c| } \hline \text { Intervals } & \text { Frequency } \\\hline Z \leq - 1.5 & 15 \\- 1.5 < Z \leq - .5 & 32 \\- .5 \leq Z \leq .5 & 65 \\.5 < Z \leq 1.5 & 25 \\Z > 1.5 & 13 \\\hline\end{array}$

Question

Suppose that a random sample of 150 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardized and the number of observations in each of the intervals below was counted. Can we infer at the 5% significance level that the data were drawn from a normal population?
 $$\begin{array} { | l | c| } 
\hline \text { Intervals } & \text { Frequency } \
\hline Z \leq - 1.5 & 15 \
- 1.5 < Z \leq - .5 & 32 \
- .5 \leq Z \leq .5 & 65 \
.5 < Z \leq 1.5 & 25 \
Z > 1.5 & 13 \
\hline
\end{array}$$

Quizplus · Accepted Answer

The Answer is H₀: p₁ = 0.0668, p₂ = 0.2417, p₃ = 0.3830, p₄ = 0.2417, p₅ = 0.0668 (The population is normal)
H₁: At least two proportions differ from their specified values (The population is not normal)
Rejection region:

\chi

² >

\chi

²_0.05,2 = 5.991
Test statistic:

\chi

² = 8.347
Conclusion: Reject the null hypothesis. We can't infer at the 5% significance level that the data were drawn from a normal population.

Suppose That a Random Sample of 150 Observations Was Drawn