Question

4- (14%) A random sample of 10 yields a mean and standard deviation, respectively, of 80 and 7.9. Does this sample confirm that the population mean is greater than 78 with 95% confidence level?

Answer 1

Solution:

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H₀: µ = 78 versus H_a: µ > 78

This is an upper tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 78

Xbar = 80

S = 7.9

n = 10

df = n – 1 = 9

c = 95% = 0.95

α = 1 - c = 1 - 0.95 = 0.05

Critical value = 1.8331

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (80 - 78)/[ 7.9/sqrt(10)]

t = 0.8006

P-value = 0.2220

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the population mean is greater than 78 with 95% confidence level.

This sample does not confirm that the population mean is greater than 78 with 95% confidence level.