A recent study focused on the number of times men and women send a WeChat messag
ID: 3019892 • Letter: A
Question
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?
Explanation / Answer
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.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.