Question

6. All of the following statements about confidence intervals are correct EXCEPT?: *
(A) Holding other numbers fixed, increasing the level of confidence will result in a wider confidence interval.
(B) Holding other numbers fixed, increasing sample size will result in a narrower confidence interval.
(C) The sample mean / proportion will always be inside the confidence interval.
(D) The population mean / proportion will always be inside the confidence interval.

7. Weight, in pounds, is measured for each person in a sample. After the data are collected, all the weight measurements are converted from pounds to kilograms by multiplying each measurement by 2.2. Which of the following statistics will remain the same for both units of measure?: *
(A) The z-scores of the weight measurements.
(B) The maximum of the weight measurements.
(C) The standard deviation of the weight measurements.
(D) The median of the weight measurements.
(E) The mean of the weight measurements.

8. The weight of a carton of strawberries has mean of 16 ounces and standard deviation of 1.5 ounces. What can you say about the distribution of the mean weight of a random sample of 41 cartons?: *
(A) Mean = 16, standard error = 1.5, unknown shape
(B) Mean = 16, standard error = 1.5, approximately normal
(C) Mean = 16, standard error = 0.234, unknown shape
(D) Mean = 16, standard error = 0.234, approximately normal

Answer 1

6.

(A)

Other numbers being fixed, increasing the level of confidence widens confidence interval.

(B)

Other numbers being fixed, increasing sample size decreases standard deviation which is multiplied with z-scores (or t-scores or anything of these types). This results in a narrowing confidence interval.

(C)

Confidence intervals are made based on sample estimates. So, the sample mean / proportion will always be inside the confidence interval.

(D)

Confidence intervals are made based on sample estimates. So, the population mean / proportion may or may not be inside the confidence interval.

Hence, (D) is not correct.

7.

(A)

The z-scores are independent of scale change.

(B)

Maximum value is dependent of scale change.

(C)

Standard deviation value is dependent of scale change.

(D)

Median value is dependent of scale change.

(E)

Mean value is dependent of scale change.

Hence, (A) The z-scores of the weight measurements.

8.

X being random variable we have,

Mean weight is given by

By law of large number (CLT), the distribution is approximately normal [approaches normal as (41 here)].

Hence, (D) is correct.