2. At a certain university the average performance by students in their introduc

Question

2. At a certain university the average performance by students in their introductory statistics class on a standardized final exam over several years was 73.5. In order to combat a decreasing budget, the department of statistics decided to combine the students into a single, large class The 151 students in the class had an average score on the same standardized final exam of 71.4 with a standard deviation of 12.4. a. Is there evidence the students performed worse, on average, than in prior years? b. In terms of the problem, what is a type I error? C. In terms of the problem, what is a type II error? d. Based on your answer to part a, which error could you have made?

Explanation / Answer

a)

Z= (x-u)/ (?/sqrt(n))

= (71.4-73.5)/(12.4/sqrt(151))

Z= -2.08

P(Z<-2.08) = 0.0188 < 0.05

If the P-value is less than (or equal to) ?,reject the null hypothesis in favor of the alternative hypothesis.

Thus, they have performed poorly

b)

type I error is the incorrect rejection of a true null hypothesis

Here, it will be assuming they are performing poorly when in reality they are not

c)

type II error is incorrectly retaining a false null hypothesis

Here, it will be assuming they are performing well even whey they are not

d)

Here, null hypothesis is reject thus possible error would have occured if we assume they are performing well even whey they are not

i.e Type II

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