Question

0 students were asked to randomly pick one of the numbers 1,2,3,4,5,6,7,8,9,10. The number 7 was picked by 57 students. (a) For the sample, calculate the proportion of students who picked 7. (Round the answer to three decimal places.) (b) Calculate the standard error for this sample proportion. (Round the answer to four decimal places.) places.) places.) places.) (f) What do the results of parts (c)-(e) indicate about the effect of confidence level on the width of a confidence interval? (Select all that apply.) As the confidence level is decreased, the width of the interval increases. As the confidence level is decreased, the width of the interval decreases. As the confidence level is increased, the width of the interval decreases. As the confidence level is increased, the width of the interval increases. (g) On the basis of these confidence intervals, do you think that students choose numbers "randomly"? Yes No

Answer 1

The proportion of students who picked the number 7 is calculated by dividing the number who picked 7 by the total number of students. The standard error for the proportion is based on the sample size and proportion. The width of a confidence interval increases with the confidence level and decreases when the confidence level is reduced.

Step-by-step explanation:

The student asked about calculating the proportion of students who picked the number 7, the standard error, and the implications of different confidence levels on the width of a confidence interval. They also questioned the randomness of number choice based on given confidence intervals.

To calculate the proportion (p-hat) of students who picked the number 7 from a sample, you divide the number of students who picked 7 by the total number of students. The standard error (SE) for a sample proportion is calculated using the formula SE = sqrt[(p-hat(1 - p-hat))/n], where p-hat is the sample proportion and n is the sample size.

Regarding confidence intervals, the width is affected by the confidence level as follows:

• As the confidence level is decreased, the width of the interval decreases.
• As the confidence level is increased, the width of the interval increases.

If the confidence intervals are not aligned with what would be expected from random selection, it might suggest that the students did not choose numbers randomly.