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?
need the answer {as early as possible}
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:
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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