Question

Consider the hypotheses below. Ho u = 50 Hu#50 Given that x = 61, s = 14, n = 16, and a = 0.01, answer the questions below. a. What conclusion should be drawn? b. Use technology to determine the p-value for this test.

I REALLY WANT TO UNDERSTAND HOW TO DO ONLY PART B!!!

The P-value is 0.007 but what formula do you use on Excel to get this answer? Please break it down for me to understand.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 50
Alternative Hypothesis: μ ≠ 50

Rejection Region
This is two tailed test, for α = 0.01 and df = 15
Critical value of t are -2.947 and 2.947.
Hence reject H0 if t < -2.947 or t > 2.947

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (61 - 50)/(14/sqrt(16))
t = 3.143

P-value Approach
P-value = 0.007
As P-value < 0.01, reject the null hypothesis.

Excel formula : =2*(1-T.DIST(3.143,15,TRUE))
T.DIST(3.143,15,TRUE) - this gives the probability of t < 3.143
As this is two tailed test, we first find the area in right tail by 1 - T.DIST(3.143,15,TRUE)
And then multiply it by 2