Question

Suppose a random sample of 150 universities is used to test the null hypothesis that the average number of spam emails economics graduate students receive in a month is

46.92.The value of the test statistic is found to be 1.02

1. If the null is tested against the alternative hypothesis that the number of spam emails is not 46.92​, the smallest significance level at which you can reject the null hypothesis is.

2. If the null is tested against the alternative hypothesis that the number of spam emails is more than 46.92​, the smallest significance level at which you can reject the null hypothesis is

Answer 1

Answer)

As the sample size is quiet large

We can use standard normal z table

1)

Null hypothesis Ho : u = 46.92

Alternate hypothesis Ha : u not equal to 46.92

Test statistics is 1.02

From z table, P(z>1.02) = 0.1539

As the test is two tailed

P-value = 2*0.1539 = 0.3078

We reject the null hypothesis when p-value is less than the significance

So, we will reject this when we will have our significance level > 0.3078

Smallest one = 0.31

B)

Here test is one tailed

So, p-value = 0.1539

So, smallest significance level = 0.16