Question

You wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02.

      Ho:μ=88.4Ho:μ=88.4
      Ha:μ<88.4Ha:μ<88.4

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=26n=26 with mean M=82.4M=82.4 and a standard deviation of SD=15.3SD=15.3.

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 p-value 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 88.4.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 88.4.
• The sample data support the claim that the population mean is less than 88.4.
• There is not sufficient sample evidence to support the claim that the population mean is less than 88.4.

Answer 1

This is the left tailed test .

The null and alternative hypothesis is

H₀ :   = 88.4

H_a : 88.4

Test statistic = t

= ( - ) / s / n

= (82.4 - 88.4) / 15.3 / 26

Test statistic = -2.00

df = 26 - 1 = 25

P-value = 0.0282

= 0.02

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 88.4.