Question

Given sample statistics: mean = 37.8; std deviation = 6; N = 144

Test the following hypotheses at a=.05

Ho: u = 39

Ha: u ne 39

You must compute the standard error and t-statistic, look up appropriate t critical value, make decision and specify possible type of error, and compute the appropriate confidence interval.

Please upload into a Microsoft Word file and show work for answers.

Answer 1

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

The null and alternative hypotheses are given as below:

H0: µ = 39 versus Ha: µ ≠ 39

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 39

Xbar = 37.8

S = 6

n = 144

df = n – 1 =

α = 0.05

Critical value = - 1.9767 and 1.9767

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (37.8 - 39)/[6/sqrt(144)]

t = -2.4

P-value = 0.0177

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

Possible type of error: Type I error

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

df = n – 1 = 144 - 1 = 143

Confidence level = 95%

Critical t value = 1.9767

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 37.8 ± 1.9767*6/sqrt(144)

Confidence interval = 37.8 ± 0.9883

Lower limit = 37.8 ± 0.9883 = 36.8117

Upper limit = 37.8 ± 0.9883 = 38.7883

Confidence interval = (36.8117, 38.7883)