Question

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

      Ho:μ=59.6Ho:μ=59.6
      Ha:μ<59.6Ha:μ<59.6

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=6n=6 with mean M=56.5M=56.5 and a standard deviation of SD=6.8SD=6.8.

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...

• 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 59.6.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 59.6.
• The sample data support the claim that the population mean is less than 59.6.
• There is not sufficient sample evidence to support the claim that the population mean is less than 59.6.

Answer 1

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (56.5 - 59.6)/(6.8/sqrt(6))
t = -1.117

p-value = 0.1574

p-value is greater than alpha

Fail to reject H0

There is not sufficient sample evidence to support the claim that the population mean is less than 59.6