A recent study focused on the number of times men and women

A recent study focused on the number of times men and women send a WeChat message in a day. The information is summarized next. At the .01 significance level, conclude on whether there is a difference in the mean number of times men and women send a Twitter message in a day.

                     Sample size         sample mean                population standard deviation

Men                   25                          23                                              5

women               30                         28                                             10

1Develop the null and alternative hypotheses for this study?

2Determine a test statistic and the critical value(s).

3) Calculate the value of the test statistic for this hypothesis testing.

4What is the p-value for this hypothesis test?

5Based on the p-value, what is your conclusion?

We know the population standard deviation, maybe we should use z test?

Solution

Answer to question# 1)

Null hypothesis: The mean number of tweets per day by men and female is same

Alternate hypothesis: The mean number of tweets per day by men and female is different

.

Answer to question# 2)

df = 25+30-2 = 53

alpha = 0.01

Two tailed test

the T critical value can be obtained by the excel formula

=t.inv.2t(0.01,53)

We get t critical = -2.6718 and +2.6718

.

Answer to question# 3)

T statistic formula is:

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

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

t = -2.4019

.

Answer to question# 4)

P value can be obtained by the excel formula

=t.dist.2t(2.4019,53)

We get P value = 0.019848

.

Answer to question# 5)

Since the P value 0.019848 < alpha 0.05 , we reject the null hypothesis. And thus conclude that the difference between the mean number of tweets of males and females per day is statistically significant.