Question

Problem #1: Researchers are interested in how many times healthcare workers at a nursing home wash their hands during the afternoon shift, and if there is a difference by sex. They separate workers into 2 groups (5 male & 6 females) and record the number of times they wash their hands during their shift. Use the data, significance chart, and hint section below to answer questions Questions a – c.

Group 1: Males	Group 2: Females
4	5
5	9
5	3
3	5
3	5
	9

Hint: Calculate means for both groups:

Identify: Calculate degrees of freedom: Sum the squared differences: Solve for variance:

M1= M2=

n1= n2= df=

∑D12 = ∑D22 = s2=

Finally, plug M1, M2, n1, n2 and s2 into t formula and solve.

a) Calculate the t-statistic: t = ______

b) Interpret the results:

• The threshold to compare the statistic at = 0.05 is _______.

• Is the difference between the groups significant or non-significant?

• Therefore, we (circle one: reject / fail to reject) the null hypothesis, and conclude that

• Males (choose one)

  • Take significantly longer to complete the assignment than females.

  • Take significantly less time to complete the assignment than females.

  • Take the exact same amount of time to complete the assignment as females.

  • Take less time to complete the assignment than females, but the difference is not
    significant.

• c) Graph the finding:
  Please label the X & Y axis

  

Answer 1

1.

Suppose, random variables X and Y denote number of hand washes of males and females respectively.

We do not know population standard deviation (or variance). So, we have to perform two sample t-test for equality of means.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistics is given by

Here,

First sample size

Second sample size

Degrees of freedom

Level of significance

So, critical value is given by

In case of lesser than alternative hypothesis we reject our null hypothesis if .

So, we cannot reject our null hypothesis.

(a)

The t-statistic: t = -1.699324

(b)

The threshold to compare the statistic at = 0.05 is -1.833113.

The difference between the groups is non-significant.

Therefore, we fail to reject the null hypothesis, and conclude that males take less time to complete the assignment than females, but the difference is not significant.

(c)

Taking t-statistic along X-axis and probability density function in Y-axis we get as follows.