Answer to Question #346268 in Statistics and Probability for John Lloyd

Question #346268

2. Don, a canteen owner claims that the average meal cost of his usual costumers

is 190 pesos. In order to test his claim, Don took a random sample of 25

costumers and found out that the meal cost is 210 with a standard deviation of

30 pesos. Test the hypothesis at 0.01 level of significance.


1
Expert's answer
2022-05-30T23:30:56-0400

The following null and alternative hypotheses need to be tested:

"H_0:\\mu=190"

"H_1:\\mu\\not=190"

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 = 0.01," "df=n-1=24" and the critical value for a two-tailed test is "t_c =2.79694."

The rejection region for this two-tailed test is "R = \\{t:|t|>2.79694\\}."


The t-statistic is computed as follows:


"t=\\dfrac{\\bar{x}-\\mu}{s\/\\sqrt{n}}=\\dfrac{210-190}{30\/\\sqrt{25}}=3.333333"


Since it is observed that "|t|=3.333333>2.79694=t_c," it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value for two-tailed, "df=24" degrees of freedom, "t=3.333333" is "p=0.002776," and since "p=0.002776<0.01=\\alpha," it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean "\\mu"

is different than 190, at the "\\alpha = 0.01" significance level.


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