Question

You wish to test the following claim (HaHa) at a significance level of α=0.01.

      Ho:μ=63.7
      Ha:μ>63.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=69 with mean M=66.9 and a standard deviation of SD=10.6.

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...

• _____less than (or equal to) αα
• _____greater than αα

This test statistic leads to a decision to...

• ____reject the null
• ____accept the null
• ____fail to reject the null

As such, the final conclusion is that...

• _____There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 63.7.
• ____There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 63.7.
• ____The sample data support the claim that the population mean is greater than 63.7.
• ____There is not sufficient sample evidence to support the claim that the population mean is greater than 63.7.

Answer 1

Solution :

= 63.7

= 66.9

s =10.6

n = 69

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :    = 63.7

H_a : > 63.7

Test statistic = t

= ( - ) / s / n

=( 66.9-63.7) /10.6 / 69

= 2.508

Test statistic = t = 2.508  

P-value =0.0073

= 0.01

P-value <

0.0073 < 0.01

Reject the null hypothesis

.There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 63.7.