Question

You wish to test the following claim (H1H1) at a significance level of α=0.05α=0.05.

      Ho:μ=67.1Ho:μ=67.1
      H1:μ<67.1H1:μ<67.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=97n=97 with mean M=64.7M=64.7 and a standard deviation of SD=14.1SD=14.1.

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 67.1.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 67.1.
• The sample data support the claim that the population mean is less than 67.1.
• There is not sufficient sample evidence to support the claim that the population mean is less than 67.1.

Answer 1

Solution :

Given that,

Population mean = = 67.1

Sample mean = = 64.7

Sample standard deviation = s = 14.1

Sample size = n = 97

Level of significance = = 0.05

This is a left tailed test.

The test statistics,

t = ( - )/ (s/)

=( 64.7 - 67.1) / ( 14.1/97)

= -1.676

P- Value = 0.0485

The p-value is p = 0.0485 < 0.05, it is concluded that reject the null hypothesis.

Conclusion :

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 67.1