Question

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here. Sample Size - Sample Mean - Population Standard Deviation Men: 25 - 23 - 5 Women: 30 - 28 - 10 At the 0.01 significance level, we ask if there is a difference in the mean number of times men and women send a Twitter message in a day. What is the value of the test statistic for this hypothesis test?

Answer 1

The value of the test statistic for this hypothesis test is approximately -2.4.

Step-by-step explanation:

To find the test statistic for this hypothesis test, we can use the two-sample t-test formula:

t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))

Where:

x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the given values:

Men: x1 = 23, s1 = 5, n1 = 25

Women: x2 = 28, s2 = 10, n2 = 30

We can now calculate the test statistic:

t = (23 - 28) / sqrt((5^2/25) + (10^2/30))

Simplifying the expression:

t = -5 / sqrt((25/25) + (100/30))

t = -5 / sqrt(1 + 10/3)

t = -5 / sqrt(1 + 3.333)

t = -5 / sqrt(4.333)

t = -5 / 2.081

t ≈ -2.4

Answer 2

There is no difference in the mean number of times men and women send a Twitter message in a day

Zmen = 0.4

Zwomen = 0.2

Step-by-step explanation:

Null hypothesis: There is no difference in the mean number of times men and women send a Twitter message in a day

Alternate hypothesis: There is a difference in the mean number of times men and women send a Twitter message in a day

Z = (sample mean - population mean)/(sd ÷ √n)

Zmen = (25 - 23)/(5÷√1) = 2/5 = 0.4

Zwomen = (30 - 28)/(10÷√1) =2/10= 0.2

For a two tailed test, at 0.01 significance level, the critical value is 2.576

0.2 and 0.4 falls within the region bounded by -2.576 and 2.576, so we fail to reject the null hypothesis

There is no difference in the mean number of times men and women send a Twitter message in a day