A random sample of 100 observations from a population with standard deviation 14

Question

A random sample of 100 observations from a population with standard deviation 14.05 yielded a sample mean of 92.4. 1. Given that the null hypothesis is =90 and the alternative hypothesis is >90 using =.05, find the following:

(a) Test statistic = 1.708185053

(b) P - value:

(c) The conclusion for this test is: A. Reject the null hypothesis B. There is insufficient evidence to reject the null hypothesis C. None of the above

2. Given that the null hypothesis is =90 and the alternative hypothesis is 90 using =.05, find the following:

(a) Test statistic = 1.708185053

(b) P - value:

(c) The conclusion for this test is: A. There is insufficient evidence to reject the null hypothesis B. Reject the null hypothesis C. None of the above

HOW DO YOU FIND P??

Explanation / Answer

1)

to find p value for this problem we need to use tables of Z distribution because we know the value

of Sigma of the population

so using Z distribution

we have the value of test statistics that is our Z = 1.71 aprox. 2 decimals

using tables of Z distribution we need to find a probability for Z = 1.71

so P value is 0.0436

The conclusion for this test is

Reject the null hypothesis

Why? because our P value is less than alpha

if P value was greater than alpha then we fail to reject the null hypothesis

but yfor this case we reject the null hypothesis

2)

to find this p value is the same as we do in the first question but something will change because the alternative hypothesis is different

when the sign is not equal to, that means that can be less than or greater than, we are talking about a 2 tailed test

that means that the decision rule will be

alpha/2 = 0.025

if P value is greater than 0.025 then , we fail to reject Ho

if P value is less than 0.025 then, we reject Ho

Pvalue is the same because Z = 1.71

P value = 0.0436

since P value is greater than 0.025 we fail to reject Ho

that means There is insufficient evidence to reject the null hypothesis

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