Question

10.4 Comparing two means: Paired samples

"We want to know if there is a difference between the size of the shoe between mother and daughter, for which a sample of 10 pairs of mother and daughter is taken and a hypothesis test is performed."

Mother	7	7	8	8	6	9	8	6	7	9
Daughter	7	6	8	6	9	8	8	7	8	7

1. State the hypotheses
2. what is the average value of the paired differences (d-bar)

3. Calculate the stadistic. T_calc

4. Do we accept or reject the null hypothesis?

Answer 1

Here, we have to use paired t test.

1. State the hypotheses

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: There is no difference between the size of the shoe between mother and daughter.

Alternative hypothesis: Ha: There is a difference between the size of the shoe between mother and daughter.

H0: µd = 0 versus Ha: µd ≠ 0

This is a two tailed test.

2. What is the average value of the paired differences (d-bar)

Dbar = 0.1000

(by using excel)

3. Calculate the test statistic.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

Dbar = 0.1000

Sd = 1.5239

n = 10

df = n – 1 = 9

α = 0.05

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (0.1000 - 0)/[ 1.5239/sqrt(10)]

t = 0.2075

Tcalculated = 0.2075

Critical values = - 2.2622 and 2.2622

The p-value by using t-table is given as below:

P-value = 0.8402

4. Do we accept or reject the null hypothesis?

P-value > α = 0.05

Test statistic value is lies between given two critical values.

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that there is a difference between the size of the shoe between mother and daughter.