Question

You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10.

      Ho:μ=53.7Ho:μ=53.7
      Ha:μ≠53.7Ha:μ≠53.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=10n=10 with a mean of ¯x=50.7x¯=50.7 and a standard deviation of s=8.7s=8.7.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±

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

The standardized test statistic is...

in the critical region

not in the critical region

This standardized 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 not equal to 53.7.

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 53.7.

The sample data support the claim that the population mean is not equal to 53.7.

There is not sufficient sample evidence to support the claim that the population mean is not equal to 53.7.

Answer 1

Solution :

Given that ,

= 50.7

= 53.7

s = 8.7

n = 10

df = n - 1 = 10 - 1 = 9

= 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,9 = 1.833

Critical value = 1.833

Test statistic = t = ( - ) / s / n

= (50.7 - 53.7) / 8.7 / 10 = -1.090

Test statistic = -1.090

Test statistic > critical value

The standardized test statistic is in the critical region .

Reject the null hypothesis .

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 53.7.