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:µ=88 vs. Ha:µ<88 .
B. H0:µ=78 vs. Ha:µ=88 .
C. H0:µ=88 vs. Ha:µ=78 .
D. H0:µ=78 vs. Ha:µ>78 .

The right option is:

D. H0:µ=78 vs. Ha:µ>78.

Step-by-step explanation:

The teacher wants to test the claim that the small class perform better than the large class.

This claim is going to be stated in the alternative hypothesis. If he want to test if the small class perform better, he means that there is evidence that their score is higher than the larger class. Then, he will test the claim that the true mean of the small class is higher than 78 (μ>78).

The null hypothesis will state that there is no significative better performance from the small class (μ=78).

Then the right option is:

D. H0:µ=78 vs. Ha:µ>78.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.