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?


1
Expert's answer
2022-06-16T06:21:22-0400

The following null and alternative hypotheses need to be tested:

H0:μ15H_0:\mu\le 15

H1:μ>15H_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 is α=0.05,\alpha = 0.05, df=n1=29df=n-1=29 and the critical value for a right-tailed test is tc=1.699127.t_c =1.699127.

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

The t-statistic is computed as follows:



t=11.9101.8/25=13.4152.98/30=2.9408t=\dfrac{11.9-10}{1.8/\sqrt{25}}=\dfrac{13.4-15}{2.98/\sqrt{30}}=-2.9408


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

Using the P-value approach:

The p-value for right-tailed, df=29df=29 degrees of freedom, t=2.9408t=-2.9408 is p=0.996814,p=0.996814, and since p=0.996814>0.05=α,p=0.996814>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 μ\mu is greater than 15, at the α=0.05\alpha = 0.05 significance level.


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