Question

A. Student study times. A class survey in a large class for first-year college students asked, "About how many hours do you study during a typical week?" The mean response of the 463 students
was Hx= 13.7 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation o= 7.4 hours in the population of all first-year students at this university

A. Use the survey result to give a 99% confidence interval for the mean study time of all first-year students.

B. What condition not yet mentioned must be met for your confidence interval to be valid​

Answer 1

Answer:

A.  12.68 - 14.72 hours

B. Normal distribution.

Step-by-step explanation:

Part A

This question is using quantitative data. A 99% confidence interval means that you want to know the range where 99% of the population will be. To find this you have to convert the 99% CI into the z-score which is -2.58SD to + 2.58SD.  

Note that the standard deviation(SD) is from the sample, not the population. We still need to find the standard deviation of the population. The formula is:

population SD = $\frac{o}{\sqrt[]{n} }$

Where the o= sample SD = 7.4

n= number of sample = 463

The calculation will be:

population SD = $\frac{o}{\sqrt[]{n} }$

population SD = $\frac{7.4}{\sqrt[]{463} }$= 0.3951

The bottom limit will be:

Mean - SD * z-score= 13.7 - 0.3951*2.58 = 12.68 hours

The upper limit will be:

Mean + SD * z-score= 13.7 + 0.3951*2.58 =14.72 hours

The 99% CI range will be 12.68 - 14.72 hours

Part B

The table used to convert confidence interval into z-score depends on the distribution type of the data. Most data is classified as normal distributed, a data type that will concentrated at mean and spread equally from the mean. Normal distribution data will look like a bell which make it also called bell curve.  

The question tells you that the data is normal distribution, but that doesn't mean every data is normally distributed. There are a lot of other data distribution type so we have to do some tests to know the normality of the data in real-life data.