Question

A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was µ=78 with standard deviation σ=10 . One year, the teacher taught a much smaller class of only 25 students. The teacher wanted to know if teaching a smaller class was more effective and students performed better. We can consider the small class as an SRS of the students who took the large class over the years. The average midterm score was x¯=83 .The hypothesis should be:a. H0:????=78 vs. H????:????>78 .

b. H0:????=88 vs. H????:????=78 .
c. H0:????=88 vs. H????:????<88 .
d. H0:????=78 vs. H????:????=88 .

Answer 1

The teacher select a sample of n =15 students. And he wanted to know if teaching a smaller class was more effective and students performed better, that means if
`\mu >78` and he obtaind a sample mean of
`\bar X>83`.

Based on this the correct system of hypothesis are:

Null hypothesis:
`\mu =78`

Alternative hypothesis:
`\mu >78`

And the best option for this case is:

a. H0:
`\mu=78` vs. H1:
`\mu>78` .

Explanation:

For this case we have the following previous info given:

`\mu = 78` represent the true mean

`\sigma =10` represent the true deviation

The teacher select a sample of n =15 students. And he wanted to know if teaching a smaller class was more effective and students performed better, that means if
`\mu >78` and he obtaind a sample mean of
`\bar X>83`.

Based on this the correct system of hypothesis are:

Null hypothesis:
`\mu =78`

Alternative hypothesis:
`\mu >78`

And the best option for this case is:

a. H0:
`\mu=78` vs. H1:
`\mu>78` .