Stats Help part a b c Thank you Assume that n 400 observat

Stats Help! ( part a b c)

Thank you!

Assume that n - 400 observations are independently drawn from a normal distribution with unknown population mean i and unknown population variance a1. The resulting sample, x, is used to test Hq i 0 at significance level a = 0.05. What test should be used in this situation? If we observe x that results in x - 3.194887 and s2 = 104.0118, then what is the value 1 of the test statistic? If we observe x that results in a test statistic value of 1.253067, then which of the following R expressions best approximates the significance probability? True or False: if we observe x that results in a significance mb ability of p = 0.03044555, then we should reject the null hypothesis.

Solution

1)

well, as you know when we know the standard deviation of the population we can use Z distribution

but when we dont know the Sd of the population then , we procceed to use T distribution ( student)

value of T = 3.194887 / srqt ( 104.0118 / 400) = 6.265

2)

iv) thats the correct answer

3)

as you can see p-value is lower than alpha ( significance level) so we should reject Ho because the probability ( p*value) is in the rejection region