Question

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

      Ho:μ1=μ2Ho:μ1=μ2
      Ha:μ1<μ2Ha:μ1<μ2

You obtain the following two samples of data.

Sample #1	Sample #2
54.9 57.4 66.1 63.7 48.9 57.4 65.2 59.3 48.9 57.9 57.6 51.8 56.3 59.6 59.4 55.1 65.8 58 49.4 64.4 65.2 52.6 62.7 58.8 56.8 62.3 59.3 54.9 61.9 52.8 53.9 62.9 60.9 54.1 62.7 54.1 62.5 54.5 64.4 58 65.2 47.6 56.9 65.8 62.7 54.1 53.3 62.3 53.3	79.6 71.4 66.3 67.5 69.2 86.3 60.6 72.8 62.1 66.6 60.3 56.9 62.9 45.6 71.4 70.1 65.2 86.3 65.5 63.8 69.5 70.4 70.4 54.9 68.3 60.9 64.4 63.8 66.9 46.8 54.5 66.3 66 86.3 70.4 66 69.5 44.1

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? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

Answer 1

Using 2 sample t test in Minitab software, we get the following output

To test against

The test statistic can be written as

which under H₀ follows a t distribution with df

where

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic

and P-value =

Plt, < tols) = P(t52 <-4.57) = 0

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that population mean for 1st sample is significantly less than that of for sample 2.