A survey of undergraduates at CAL STATE asked a random sample of 75 students abo

Question

A survey of undergraduates at CAL STATE asked a random sample of 75 students about the amount they had spent on textbooks (in dollars) during the current term. The 95% confidence interval created from this data was $370 ± $35. This interval indicates: Select all that apply. Select one or more: A) That the average of all undergraduate students at this university must be $370. B) That if we take many samples from this population 95% of them will have a sample mean between $335 and $405. C) That 95% of all undergraduate students at this university spent between $335 and $405 on textbooks this term. D) That $35 is 95% of the true average for all undergraduate students. E) The standard deviation of the sample is about 5% smaller than the population standard deviation. F) The average of the 75 students sampled is definitely between $335 and $405. G) We are 95% confident that the average for the 75 students sampled is between $335 and $405. H) We are 95% confident that the average for all CAL STATE undergraduate students is between $335 and $405. I) The parent population is skewed and thus 5% of the students spent less than $335 or greater than $405 on textbooks. *** There are similar questions on Chegg, but some of the answers appear incorrect or justification is incomplete. ***

Explanation / Answer

Given the CI

$370 ± $35

this means the upper and lower limit of the range is 405 , 335

Select one or more:

A) That the average of all undergraduate students at this university must be $370. not true , but we are 95% confident that this mean value would lie between 335 and 405

B) That if we take many samples from this population 95% of them will have a sample mean between $335 and $405.

true , this is what the confidence interval means

C) That 95% of all undergraduate students at this university spent between $335 and $405 on textbooks this term.

no , this doesnt mean that 95% of the population spent between 335 and 405

D) That $35 is 95% of the true average for all undergraduate students.

not true , doesnt make any sense

E) The standard deviation of the sample is about 5% smaller than the population standard deviation.

F) The average of the 75 students sampled is definitely between $335 and $405.

yes , because we have accounted for the sample error given by SE = SD/sqrt(n), where N is the sample size

G) We are 95% confident that the average for the 75 students sampled is between $335 and $405.

no , we are sure that average of the sample is 370

H) We are 95% confident that the average for all CAL STATE undergraduate students is between $335 and $405.
True

I) The parent population is skewed and thus 5% of the students spent less than $335 or greater than $405 on textbooks

we cant say this unless we get to see the shape of the distribution of the data

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