Question

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

      Ho:μ=80.9Ho:μ=80.9
      Ha:μ<80.9Ha:μ<80.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=4n=4 with mean M=72.1M=72.1and a standard deviation of SD=8.8SD=8.8.

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... (select one)

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...( select one)

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...(select one)

• There is sufficient evidence to warrant rejection of the claim that the population mean is less than 80.9.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 80.9.
• The sample data support the claim that the population mean is less than 80.9.
• There is not sufficient sample evidence to support the claim that the population mean is less than 80.9.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 80.9

H_a : < 80.9

= 72.1

= 80.9

s = 8.8

n = 4

df = 4 - 1 = 3

Test statistic =t

= ( - ) / s / n

= (72.1 - 80.9) / 8.8 / 4

= -2

Test statistic = -2

P-value = 0.0697

= 0.10

P-value <

Reject the null hypothesis .

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 80.9.