Answer:
The value of the test statistic = 2.58
Test statistic Z = - 4.805
|Z| = 4.805 > 2.58
Null hypothesis is rejected The value of the test statistic = 2.58
There is significant difference between in the mean number of times men and women send a Twitter message in a day
Step-by-step explanation:
Step(i):-
Sample size of men n₁ = 25
mean of the first sample x₁⁻ = 20
Standard deviation of the first sample σ₁ = 5
Sample size of women n₂ = 30
mean of the second sample x₂⁻ = 30
Standard deviation of the first sample σ₂ = 10
Level of significance ∝= 0.01
<u>Step(ii)</u>:-
Null Hypothesis : H₀: There is no significant difference between in the mean number of times men and women send a Twitter message in a day
Alternative Hypothesis :H₁:There is significant difference between in the mean number of times men and women send a Twitter message in a day
Test statistic
![Z = \frac{x^{-} _{1} - x^{-} _{2} }{\sqrt{\frac{S.D_{1} ^{2} }{n_{1} }+\frac{ S.D_{2} ^{2}}{n_{2} } } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bx%5E%7B-%7D%20_%7B1%7D%20-%20x%5E%7B-%7D%20_%7B2%7D%20%7D%7B%5Csqrt%7B%5Cfrac%7BS.D_%7B1%7D%20%5E%7B2%7D%20%7D%7Bn_%7B1%7D%20%7D%2B%5Cfrac%7B%20S.D_%7B2%7D%20%5E%7B2%7D%7D%7Bn_%7B2%7D%20%7D%20%20%7D%20%7D)
![Z = \frac{20 - 30 }{\sqrt{\frac{(5)^{2} }{25 }+\frac{ (10)^{2} }{ 30} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B20%20-%2030%20%7D%7B%5Csqrt%7B%5Cfrac%7B%285%29%5E%7B2%7D%20%20%7D%7B25%20%7D%2B%5Cfrac%7B%20%2810%29%5E%7B2%7D%20%20%7D%7B%2030%7D%20%20%7D%20%7D)
Z = ![\frac{-10}{2.081} = - 4.805](https://tex.z-dn.net/?f=%5Cfrac%7B-10%7D%7B2.081%7D%20%3D%20-%204.805)
The value of the test statistic = 2.58 C
|Z| = 4.805 > 2.58
Null hypothesis is rejected The value of the test statistic = 2.58
<u>Conclusion:</u>-
There is significant difference between in the mean number of times men and women send a Twitter message in a day