Question

Based on the sample information below, test to determine if the mean number of movies watched each month differed between males and females. Use a level of significance of 0.05 and assume unequal variances.

(a) Ho and Ha

(b) Test method, test statistic, and p-value

(c) Statistical decision and case-specific conclusion

	Female	Male
Mean number of movies watched /month	5.5	7.5
Standard deviation	2.5	4.5
Size	20	20

Answer 1

ANSWER::

a)

Null Hypothesis (H0): Mean Number of movies watched by females is equal to the Mean Number of movies watched by males

Alternative Hypothesis (Ha): Mean Number of movies watched by females is not equal to the Mean Number of movies watched by males

b)

Here we will use a t-test for two samples with unequal variance.

Consider Females as Group 1 and Males as Group 2

Test Statistic is given by:

denotes the sample mean for the females.

denotes the sample mean for the males.

denotes sample standard deviation for females.

denotes sample standard deviation for males

n1 and n2 are the respective sample sizes.

t = -1.7374

The p-value is 0.0927.

c)

The critical value for this two-tailed test is tc​=2.043, for α=0.05

Since it is observed that ∣t∣=1.737 ≤ tc​=2.043, it is then concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level.

Conclusion:

We fail to reject the null hypothesis, that means Mean Number of movies watched by females is equal to the Mean Number of movies watched by males

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