Question

You wish to test the following claim (HaHa) at a significance level of α=0.005.

      Ho:μ=52.6Ho
      Ha:μ>52.6Ha

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=27 with mean M=54.7 and a standard deviation of SD=8.4.

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 greater than 52.6.
• ______There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 52.6.
• ______The sample data support the claim that the population mean is greater than 52.6.
• ______There is not sufficient sample evidence to support the claim that the population mean is greater than 52.6.

Answer 1

Test statistics

t = ( - ) / (S / sqrt(n) )

= (54.7 - 52.6 ) / (8.4 / sqrt(27) )

= 1.299

This is test statistics value.

From T table,

With test statistics 1.299 and df of 26 ,

p-value = 0.1027

p-value is greater than

This test statistics leads to decision to fail to reject the null

Conclusion -

There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 52.6