Question

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002.

      Ho:μ=63.9Ho:μ=63.9
      H1:μ<63.9H1:μ<63.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

data

82.5

57.8

79.7

47.4

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 63.9.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 63.9.
• The sample data support the claim that the population mean is less than 63.9.
• There is not sufficient sample evidence to support the claim that the population mean is less than 63.9.

Answer 1

Given that    Ho:μ=63.9
      H1:μ<63.9

using TI 84 calculator

enter the data given data set in L1

press stat then tests then select TTest

select data L1

press calculate

we get

test statistic = 0.346

p value = 0.3761

p value is greater than alpha(0.002)

we failed to reject Ho because p value is greater than significance level

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 63.9.