A recent national survey found that high school students watched an average (mea
ID: 3312894 • Letter: A
Question
A recent national survey found that high school students watched an average (mean) of 7.0 movies per month with a population standard deviation of 0.6. The distribution of number of movies watched per month follows the normal distribution. A random sample of 43 college students revealed that the mean number of movies watched last month was 6.5. At the 0.05 significance level, can we conclude that college students watch fewer movies a month than high school students? A) State the null hypothesis and the alternative hypothesis. B) State the decision rule C) Test Statistic D) decision regrading H0 E) What is the P Value?
Explanation / Answer
Solution:
Given that x = 6.5, = 7.0
= 0.6, n = 43
= 0.05
A) Test Hypothesis:
null hypothesis H0: 7.0
Alternative hypothesis Ha: < 7.0
B) = 0.05
Z/2 = Z0.025 = 1.96
The decision rule is ,
If Test statistic -zcrit (= -1.96) , then reject the null hypothesis H0.
C) Test statistic:
Z = x - /(/n)
= 6.5- 7.0/(0.6/43)
= -5.46
D) Since, the calculated value is less than the critical value. Hence, the null hypothesis should be rejected.
E) P-value = 0.0001
Here, P-value < = 0.05. Hence, the null hypothesis should be rejected.
Thereforem it can be concluded that there is sufficient evidence to support that the mean number of DVDs watched is less than 7.0 per month.