Answer to Question #191709 in Statistics and Probability for Hazel

Question

the head of the math department claims that the mean height of grade 7 students is 163 cm. the mean height of randomly selected grade 7 students is 161 cm. using 0.05 significance level can it be concluded that the mean height of grade 7 students is shorter than 163 cm?

Answer 1

Null and alternate hypothesis:

Null Hypothesis: $H_0:\mu=161$

and Alternate Hypothesis $H_1:\mu<161$

Choose $α=.05$ The critical value for this one tailed test is 1.64. Any test statistic greater than 1.64 will be in the rejection region.

Next, we calculate the test statistic for the sample of $7^{th}$ graders.

$z=\dfrac{163-161}{\frac{7}{\sqrt{45}}}=\dfrac{2}{1.0435}=1.9166$

P- value:

$P(z<1.92)$

Using a z-score table:

$P(z<1.92)=0.9726>0.05$

The probability of observing a test statistic at least as big as the z=1.92 is 0.9726. Since this is greater than our significance level, 0.05, we fail to reject the null hypothesis. This means that the data does not support the claim that the mean is less than 161.