Astatistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. a sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. you are given the following results. today 5 years ago mean 82 88 variance 112.5 54 sample size 45 36 1) the standard deviation of the difference between the means of the two populations is a) 12.9 b)9.3 c) 4 d) 2 2) the 95% confidence interval for the difference between the two pop. means is a) -9.92 to -2.08 b)-3.92 to 3.92 c) -13.84 to 1.84 d) -24.228 to 12.23 3) the test statistic for the difference between the two pop. means is a) -0.47 b) -0.65 c) -1.5 d) -3.0 4)the p-value for the difference between the two pop. means is a) 0.0014 b) 0.0028 c) 0.4986 d) 0.9972 5) what is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (use a .05 level of significance) a) there is a statistically significant difference in the average final examination scores between the two classes. b)there is no statistically significant difference in the average final examination scores between the two classes. c) it is impossible to make a decision on the basis of the information given d) there is a difference, but it is not significant

1) D) 2

2) A) -9.92 to -2.08

3)  D) -3

4) B) 0.0028

5) A) There is a statistically significant difference in the average final examination scores between the two classes

Step-by-step explanation:

The standard deviation s of the difference between the means of the two populations can be calculated as:

Where is the variance of the first sample,   is the variance of the second sample, n1 is the size of the first sample and n2 is the size of the second sample. So, The standard deviation of the difference between the means of the two populations is:

A 95% confidence interval for the difference between the two pop. means can be calculated as:

Where (x1-x2) is the difference between the two sample means, 1-α is equal to 95% and (m1-m2) is the difference between the two population means.

Then, replacing, x1 by 82, x2 by 88, s by 2 and by 1.96, we get:

-6 - 3.92 ≤ m1-m2 ≤ -6 + 3.92

-9.92 ≤ m1-m2 ≤ -2.08

On the other hand, we can formulate a test hipotesis as:

H0: m1-m2 = 0

H1: m1-m2 ≠ 0

So, the test statistic for the difference between the two pop. means can be calculated as:

Replacing the values, we get:

Therefore, the p-value for the difference between the two pop. means can be calculated as:

p-value = 2P(Z<-3) = 2(0.0014)=0.0028

Where the probability P(Z<-3) is founded on a z-score table.

Then, if the p-value is less than the level of significance, we can reject the null hypothesis or H0 and said that there is a statistically significant difference in the average final examination scores between the two classes.

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