Answer to Question #183499 in Statistics and Probability for Mads Mendes

Question

 State the null hypothesis and the alternative hypothesis in (a) words and in 

(b) symbols for each of the following. 

a. A librarian of a school claims that all their grade 8 students read an 

average of 10 storybooks a month with a standard deviation of 2 books. 

A random sample of grade 8 students read an average 12 books a month 

and a standard deviation of 1 book. The confidence statement is 95%. 

b. According to a factory employer, the mean working time of workers in 

the factory is 6 hours with a standard deviation of 0.5 hours. A 

researcher interviewed 50% of the employees and found out that their 

mean working time is 8 hours with a standard deviation of 1 hour. The a 

level is 0.05. 

Answer 1

a.

Null hypothesis: The average number of storybooks that grade 8 students read in a month is 10.

Alternative hypothesis: The average number of storybooks that grade 8 students read in a month is not 10.

$H_0 : \mu = 10 \\ H_1 : \mu ≠ 10$

b.

Null hypothesis: The mean working time of workers in the factory is 6 hours.

Alternative hypothesis: The mean working time of workers in the factory is not 6 hours.

$H_0 : \mu = 6 \\ H_1 : \mu ≠ 6$