Question

You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005.

      Ho:μ=54.6Ho:μ=54.6
      Ha:μ>54.6Ha:μ>54.6

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=83n=83 with mean M=58.7M=58.7 and a standard deviation of SD=8.9SD=8.9.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = _____

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = ______

The p-value is...

A) less than (or equal to) αα

B)greater than αα

This test statistic leads to a decision to...

A) reject the null

B)accept the null

C) fail to reject the null

As such, the final conclusion is that...

A)There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 54.6.

B)There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 54.6.

C)The sample data support the claim that the population mean is greater than 54.6.

D) There is not sufficient sample evidence to support the claim that the population mean is greater than 54.6.

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 = 54.6 versus H_a: µ > 54.6

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 = 54.6

Xbar = 58.7

S = 8.9

n = 83

df = n – 1 = 82

α = 0.005

Critical value = 2.6371

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (58.7 - 54.6)/[8.9/sqrt(83)]

t = 4.1969

Test statistic = 4.197

P-value = 0.0000

(by using t-table)

The p-value is...

P-value < α = 0.005

A) less than (or equal to) α

So, we reject the null hypothesis

This test statistic leads to a decision to...

A) reject the null

As such, the final conclusion is that...

B)There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 54.6.