Question

You wish to test the following claim (Ha) at a significance level of α=0.05

      Ho:μ=84.2
      Ha:μ<84.2

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=4 with mean M=82.7 and a standard deviation of SD=6.1.

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 84.2.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 84.2.
• The sample data support the claim that the population mean is less than 84.2.
• There is not sufficient sample evidence to support the claim that the population mean is less than 84.2.

Answer 1

Solution :

This is the left tailed test .

Test statistic = t

= ( - ) / s / n

= (82.7 - 84.2) /6.1 / 4

= -0.491

Test statistic = -0.491

n = 4

df = n - 1 = 4 - 1 = 3

P-value using t table is,

P-value = 0.3286

= 0.05

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 84.2.