Question

You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01.

      Ho:μ=89.6Ho:μ=89.6
      Ha:μ<89.6Ha:μ<89.6

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=35n=35 with mean M=78.4M=78.4 and a standard deviation of SD=15.8SD=15.8.

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 89.6.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 89.6.
• The sample data support the claim that the population mean is less than 89.6.
• There is not sufficient sample evidence to support the claim that the population mean is less than 89.6.

Answer 1

Solution:

This is a left tailed test,

The test statistics,

t =( - )/ (s /n)

= ( 78.4 - 89.6 ) / ( 15.8 / 35 )

= -4.194

P-value = 0.0001

P-value < 0.01

Reject the null hypothesis,

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 89.6.