Question #341653

According to a study conducted by grade 11 students, Php155 is the monthly expense for cellphone loads of high school students on their province. A statistics students claims that this amount has increased since January of this year. Do you think his claim is acceptable if a random sample of 50 students has an average monthly expense of Php165 on cellphone loads? Using 0.05 level of significance, assume that a population standard deviation of Php52.

1
Expert's answer
2022-05-17T23:04:21-0400

The following null and alternative hypotheses need to be tested:

H0:μ155H_0:\mu\le155

H1:μ>155H_1:\mu>155

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is α=0.05,\alpha = 0.05, and the critical value for a right-tailed test is zc=1.6449.z_c = 1.6449.

The rejection region for this right-tailed test is R={z:z>1.6449}.R = \{z:z> 1.6449\}.

The z-statistic is computed as follows:


z=xˉμσ/n=16515552/501.35982z=\dfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{165-155}{52/\sqrt{50}}\approx1.35982

Since it is observed that z=1.35982<1.6449=zc,z=1.35982<1.6449=z_c, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach:

The p-value is p=P(z>1.35982)=0.086943,p=P(z>1.35982)=0.086943, and since p=0.086943>0.05=α,p=0.086943>0.05=\alpha, it is concluded that the null hypothesis is not rejected.

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

is greater than 155, at the α=0.05\alpha = 0.05 significance level.



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