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elena-s [515]
3 years ago
15

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized below

.
Men Sample size-25 Sample mean-20 Population standard deviation-5
Women Sample size-30 Sample mean-30 Population standard deviation-10
At the .01 significance level, is there 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?
1. 2.668
2. 2.672
3. 2.58
4. 2.40
Mathematics
1 answer:
jok3333 [9.3K]3 years ago
7 0

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} }  } }

Z = \frac{20 - 30 }{\sqrt{\frac{(5)^{2}  }{25 }+\frac{ (10)^{2}  }{ 30}  } }

Z =  \frac{-10}{2.081} = - 4.805

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

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