Question

Find the p-value for the hypothesis test. A random sample of size 53 is taken. The sample has a mean of 369 and a standard deviation of 84.

H0: µ = 400

Ha: µ< 400

The p-value for the hypothesis test is .

Your answer should be rounded to 4 decimal places.

Answer 1

Solution :

This is the left tailed test,  

The null and alternative hypothesis is ,

H0 :   = 400

Ha : < 400

Test statistic = t =

= ( - ) / s / n

= (369 - 400) / 84 / 53

Test statistic = t = -2.69

degrees of freedom = n - 1 = 53 - 1 = 52

P(t < -2.69 )

P-value = 0.0048