(Statistics) - related to p- value, confidence intervals, test statistic (z-test

Question

(Statistics) - related to p- value, confidence intervals, test statistic (z-test), null and alternative hypothesis, etc.

* 1. You randomly sample 10 students taking math 101. To what (if any) population can you make inference?

* 2. You select the 10 students sitting in the front row of economic 101. To what (if any) population can you make inference?

Please answer two questions and explain the reason.

(True/False) - 3 problems

1. If a two-sided p-value of 0.04 for a test of the null hypothesis that the population mean is 20,

I would reject the null hypothesis that the population mean is 20 vs. a two-sided alternative at level = 0.05. (True or false ?)

2. If a two-sided p-value of 0.04 for a test of the null hypothesis that the population mean is 20,

the value 20 will be in the 95% confidence interval for the population mean. (True or false ?)

3. If a two-sided p-value of 0.04 for a test of the null hypothesis that the population mean is 20,

the value 20 will be in the 90% confidence interval for the population mean. (True or false ?)

Thank you very much!

Explanation / Answer

1. If a two-sided p-value of 0.04 for a test of the null hypothesis that the population mean is 20,

I would reject the null hypothesis that the population mean is 20 vs. a two-sided alternative at level = 0.05

ans : H0 : The population mean is 20

H1 : The population means is not 20 , so at an alpha =0.05 , if the p value is less than 0.05 we reject the null hypothesis in favor of alternate hypothesis

Hence True

2. If a two-sided p-value of 0.04 for a test of the null hypothesis that the population mean is 20,

the value 20 will be in the 95% confidence interval for the population mean.

ans : H0 : The population mean is 20

H1 : The population means is not 20 , so at an alpha =0.05

as alpha is 0.05 , so the confidence interval is 100-5= 95% , so this is a direct relationship if p value is less than 0.05 this means that it is not 20 , hence it would not contain 20 , hence False

3

Using the same logic as above, the corresponding significance level for the significance test is 10%; 1 – 0.9 = 0.1 = . Since the p-value is 0.04, 0.04 < 0.1, we reject the null hypothesis, again we would find that the interval would not contain 20. , hence false

the frst 2 parts of the questions are not clear . Kindly provide more information as to what exactly is being asked .

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