Question

Assume that the population variance is unknown. We test the hypothesis that Ho: µ=5 against the alternative that it is not at a level of significance of 5% and a sample size of n=151. We calculate a test statistic = -1.976. The p-value of this hypothesis test is approximately ? . (Write your answer out to two decimal places. In other words, write 5% as 0.05.)

Answer 1

Answer

As Population Variance is unknown this means we will use t test.

Here,

Null Hypothesis : µ = 5

Alternate : µ not equals to 5 ( i.e. µ > 5 or µ < 5)

As we have to  test the hypothesis that Ho: µ=5 against the alternative (µ > 5 or µ < 5), we will use two tail test.

Hence we have to find the area to the left of -1.976 and to the right of 1.976

We can see from the t table area to the right of 1.976 with degrees of freedom n - 1 (= 151 - 1 = 150) = 0.025. Due to symmetry area to the left of -1.976 is also equals 0.025.

Hence Sum total of Area = 0.025 + 0.025 = 0.05. This is what we called p value.

Hence p value is approximately equal to 0.05

Hence, p value = 0.05