Question

EVERY ANSWER POSTED HAD SOME WRONG THINGS

A report says that 82% of British Columbians over the age of 25 are high school graduates. A survey of randomly selected British Columbians included 1290 who were over the age of 25, and 1135 of them were high school graduates. Does the city’s survey result provide sufficient evidence to contradict the reported value, 82%?

Part i) What is the parameter of interest?

A. All British Columbians aged above 25.
B. The proportion of all British Columbians (aged above 25) who are high school graduates.
C. The proportion of 1290 British Columbians (aged above 25) who are high school graduates.
D. Whether a British Columbian is a high school graduate.

Part ii) Let p be the population proportion of British Columbians aged above 25 who are high school graduates. What are the null and alternative hypotheses?

A. Null: p=0.82. Alternative: p=0.88.
B. Null: p=0.88. Alternative: p≠0.88.
C. Null: p=0.82. Alternative: p≠0.82.
D. Null: p=0.88. Alternative: p>0.88.
E. Null: p=0.88. Alternative: p≠0.82.
F. Null: p=0.82. Alternative: p>0.82.

Part iii) The P-value is less than 0.0001. Using all the information available to you, which of the following is/are correct? (check all that apply)

A. The observed proportion of British Columbians who are high school graduates is unusually low if the reported value 82% is incorrect.
B. The observed proportion of British Columbians who are high school graduates is unusually high if the reported value 82% is incorrect.
C. Assuming the reported value 82% is incorrect, it is nearly impossible that in a random sample of 1290 British Columbians aged above 25, 1135 or more are high school graduates.
D. The observed proportion of British Columbians who are high school graduates is unusually low if the reported value 82% is correct.
E. The observed proportion of British Columbians who are high school graduates is unusually high if the reported value 82% is correct.
F. The reported value 82% must be false.
G. Assuming the reported value 82% is correct, it is nearly impossible that in a random sample of 1290 British Columbians aged above 25, 1135 or more are high school graduates.

Part iv) What is an appropriate conclusion for the hypothesis test at the 5% significance level?

A. There is sufficient evidence to contradict the reported value 82%.
B. There is insufficient evidence to contradict the reported value 82%.
C. There is a 5% probability that the reported value 82% is true.
D. Both A. and C.
E. Both B. and C.

Part v) Which of the following scenarios describe the Type II error of the test?

A. The data suggest that reported value is incorrect when in fact the value is incorrect.
B. The data suggest that reported value is correct when in fact the value is incorrect.
C. The data suggest that reported value is incorrect when in fact the value is correct.
D. The data suggest that reported value is correct when in fact the value is correct.

Part vi) Based on the result of the hypothesis test, which of the following types of errors are we in a position of committing?

A. Type I error only.
B. Type II error only.
C. Neither Type I nor Type II errors.
D. Both Type I and Type II errors.

Answer 1

from the given data of information

A report says that 82% of brithish columbians over the age of 25% are high school gradutes

1290 BRITISH COLUMBIANS WERE OVER THE AGE OF 25

1135 of them were high school graduates

(1). the parameter of interest is

answer: the proportion of all british columbians (aged above 25) who are high school graduates.

option b is correct

(2). let p be the population proportion of british columbians aged above 25 who are high school graduates.what are the null and alternative hypotheses

answer: NULL: P= 0.82. Alternative: P 0.82

option c is correct

(3).the p value is less than 0.000. using all the information available to you

answer: assuming the reported value 82% is correct, it is nearly impossible that in a random sample of 1290 british columbians aged above 25, 1135 or more are high school graduates

the observed proportion of british columbians who are high school graduates is unusually high if the reported value 82% is correct.

option b and g are correct

(4). what is an appropriate conclusion for the hypothesis test at the 5% significance level

point estimate for the proportion

= 0.88

Z =

test statistic =

z = 0.88 - 0.82 /

= 5.61

pvalue <0.0001

there is sufficient evidence to contradict the reported value 82%

option a is correct

(5). answer:

in statistical hypothesis testing, a type 1 error is the incorrect rejection of a true null hypothesis

option c is correct.

(6). answer:

as in the test we are rejecting the null hypothesis and accepting the alternative hypothesis

option a is correct