Question

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

      Ho:μ=63.1Ho
      Ha:μ<63.1Ha

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=67 with mean M=54.6 and a standard deviation of SD=20.4.

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 less than 63.1.
• _____There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 63.1.
• _____The sample data support the claim that the population mean is less than 63.1.
• _____There is not sufficient sample evidence to support the claim that the population mean is less than 63.1.

Answer 1

Test statistics

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

= (54.6 - 63.1) / (20.4 / sqrt(67) )

= -3.411

From T table,

with test statistics -3.411 and df of 66,

p-value = 0.0006

The p-value is less than (or equal to )

This test statistics leads to decision to reject the null

Conclusion -

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 63.1.