Answer to Question #264516 in Statistics and Probability for Razin

Question #264516

The height of 10 students selected at a random from a school had a mean 116cm and SD 96cm.Is the group mean being different from the speculated population mean of 120cm?


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Expert's answer
2021-11-12T15:36:51-0500

The following null and alternative hypotheses need to be tested:

"H_0:\\mu=120"

"H_1:\\mu\\not=120"

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

Based on the information provided, the significance level is "\\alpha = 0.05,"  "df=n-1=10-1=9" degrees of freedom, and the critical value for a two-tailed test is "t_c =2.262156"

The rejection region for this two-tailed test is "R = \\{t: |t| > 2.262156\\}."

The t-statistic is computed as follows:


"t=\\dfrac{\\bar{x}-\\mu}{s\/\\sqrt{n}}=\\dfrac{116-120}{96\/\\sqrt{10}}=-0.131762"

Since it is observed that"|t| = 0.131762< 2.262156=t_c," it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value for two-tailed, "\\alpha=0.05, df=9" degrees of freedom, "t=-0.131762" is "p=0.898071," and since "p=0.898071>0.05=\\alpha," it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean "\\mu" is different than "120," at the "\\alpha = 0.05" significance level.


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