Question

A research organization reported that 41 percent of adults who were asked to describe their day responded that they were having a good day rather than a typical day or a bad day. To investigate whether the percent would be different for high school students, 600 high school students were randomly selected. When asked to describe their day, 245 students reported that they were having a good day rather than a typical day or a bad day. Do the data provide convincing statistical evidence that the proportion of all high school students who would respond that they were having a good day is different from 0.41 ?

A) No, because the p value is less than any reasonable significance level
B) No, because the pvalue is greater than any reasonable significance level
C) Yes, because the p-value is less than any reasonable significance level
D) Yes, because the pvalue is greater than any reasonable significance level
E) Yes, because the expected value of the number of students who will report having a good day is 246, not 245.

Answer 1

B) No, because the p-value is greater than any reasonable significance level

Explanation:

H-null: p = 0.41

H-alt: p =/= 0.41

1 proportion Z test

On a calculator: stat + tests + 5

p: .41

x: 245

n: 600

prop: =/= p

This gives a p-value = .934

(standard significance level is .05, so this p-value is much larger)

fail to reject H-null