Question #350889

A soda manufacturer is interested in determining whether it's bottling machine tends to overfill. Each bottle is supposed to contain 15 ounces of fluid. A random sample of 30 bottles was taken and found that the mean amount of soda of the sample of bottles is 13.4 ounces with a standard deviation of 2.98 ounces. if the manufacturer decides on a significance level od 0.05 test, should the null hypothesis be rejected?

Expert's answer

The following null and alternative hypotheses need to be tested:

"H_0:\\mu\\le 15"

"H_1:\\mu>15"

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 = 0.05,"Â "df=n-1=29"Â and the critical value for a right-tailed test isÂ "t_c =1.699127."

The rejection region for this right-tailed test isÂ "R = \\{t:t>1.699127\\}."

The t-statistic is computed as follows:

Since it is observed thatÂ "t=-2.9408<1.699127=t_c,"Â it is then concluded thatÂ the null hypothesis is not rejected.

Using the P-value approach:

The p-value for right-tailed,Â "df=29"Â degrees of freedom,Â "t=-2.9408"Â isÂ "p=0.996814,"Â and sinceÂ "p=0.996814>0.05=\\alpha,"Â it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population meanÂ "\\mu"Â is greater than 15, at theÂ "\\alpha = 0.05"Â significance level.

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