Question

A random sample of 100 observations from a quantitative population produced a sample mean of 30.8 and a sample standard deviation of 7.8. Use the p-value approach to determine whether the population mean is different from 32. Explain your conclusions. (Use α = 0.05.)

Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)

z =

p-value =

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 32

Ha : 32

Test statistic(z)

= ( - ) / / n

= (30.8 - 32) / 7.8 / 100

Test statistic = -1.54

P(z < - 1.54) = 2 * P(z < -1.54) = 2 * 0.0618

P-value = 0.1236

= 0.05

P-value >

Fail to reject the null hypothesis .