Question

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.

      Ho:μ=56.8Ho:μ=56.8
      Ha:μ<56.8Ha:μ<56.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=786n=786 with a mean of M=56.1M=56.1 and a standard deviation of SD=14.1SD=14.1.

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

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

The test statistic is...

• in the critical region
• not in the critical region

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 less than 56.8.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 56.8.
• The sample data support the claim that the population mean is less than 56.8.
• There is not sufficient sample evidence to support the claim that the population mean is less than 56.8.

Answer 1

Solution :

This is the left tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 56.8

H_a : < 56.8

degrees of freedom = n - 1 = 786 - 1 = 785

= 0.002

P(t < t) = 0.002

= P(t < -2.887 ) = 0.002  

critical value = t < -2.887

  

Test statistic = t =

= ( - ) / s / n

= (56.1 - 56.8) / 14.1 / 786

Test statistic = t = -1.392

The test statistic is not in the critical region

This test statistic leads to a decision to reject the null.

test statistic > critical value

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 56.8