Question

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002.

      Ho:μ=51.3Ho:μ=51.3
      H1:μ<51.3H1:μ<51.3

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=627n=627 with mean ¯x=49.8x¯=49.8 and a standard deviation of s=8.9s=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...

• 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 less than 51.3.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 51.3.
• The sample data support the claim that the population mean is less than 51.3.
• There is not sufficient sample evidence to support the claim that the population mean is less than 51.3.

Answer 1

Solution :

This is the left tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 51.3

H_a : < 51.3

Test statistic = t =

= ( - ) / s / n

= (49.8 - 51.3) / 8.9 / 627

Test statistic = t = -4.220

degrees of freedom = n - 1 = 627 - 1 = 626

P(t < -4.220)

P-value = 0

α = 0.002.

The p-value is less than (or equal to) α

This test statistic leads to a decision to reject the null

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 51.3