Question #350891

A TV manufacturer claims that the life span of its regular TV sets is longer than 10 years. Using a random sample of their 25 TV sets, the average life span is found to be 11.9 years with a standard deviation of 1.8 years. Test the hypothesis that the TV sets' life span is longer than 10 years at cx = 0.10

Expert's answer

The following null and alternative hypotheses need to be tested:

"H_0:\\mu=10"

"H_1:\\mu>10"

This corresponds to a right-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 isÂ "\\alpha = 0.10,"Â "df=n-1=24"Â and the critical value for a right-tailed test isÂ "t_c =1.317836."

The rejection region for this right-tailed test isÂ "R = \\{t:t>1.317836\\}."

The t-statistic is computed as follows:

Since it is observed thatÂ "t=5.2778>1.317836=t_c,"Â it is then concluded thatÂ the null hypothesis is rejected.

Using the P-value approach:

The p-value for right-tailed,Â "df=24"Â degrees of freedom,Â "t=5.2778"Â isÂ "p=0.00001,"Â and sinceÂ "p=0.00001<0.10=\\alpha,"Â it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population meanÂ "\\mu"Â is greater than 10, at theÂ "\\alpha = 0.10"Â significance level.

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