Use the calculators from our course when you need to calculate the Five-Number Summary, Mean, Standard Deviation, confidence intervals, P-values, or work with the Normal model.
3. For this problem, be sure to show the calculations you are making, in addition to your final answer.
According to insidehighered.com, we have the following data for US student enrollment in Fall 2020:
• Approximately 72.7% of all students took at least one distance education course
• Approximately 55% of all students took at least one in-person course
• Approximately 28% of all students took both distance education courses and
in-person courses
Note: 1) There is overlap in the student groups listed above.
2) Distance education courses include online and hybrid courses.
a. If 5 students were randomly selected from all US students in Fall 2020, find the probability that all 5 students took at least one distance education class.
b. If 1 student is randomly selected from all US students in Fall 2020, find the probability that the student only took in-person courses (took at least one in- person course, but did not take any distance education courses).
c. If 1 person is randomly selected from the students that took at least one distance education course in Fall 2020, find the probability that the student also took at least one in-person course.
4. According to the year 2020 US census results, 50% of American adults live with a spouse.
a. Assuming the necessary conditions are satisfied, give the mean and standard deviation of the Normal model that would be used to approximate the sampling distribution of the sample proportion living with a spouse for a random sample of 110 American adults.
b. Sketch by hand and clearly label the Normal model for the sampling distribution of the sample proportion from part a, based on the 68-95-99.7 Rule. Be sure to label your axis with what the variable in the sampling distribution represents.
c. Find the probability that a random sample of 110 American adults has proportion living with a spouse of 52.73% or higher.
(To show your work: Write down which calculator you are using and what values you are entering into the calculator.)
5. According to the year 2020 US census results, 50% of American adults live with a spouse. Suppose that researchers believe that the percentage of married adults may be higher in the state of Nebraska and decide to conduct a study with a random sample of adults from Nebraska to understand this further.
a. Define the parameter, and write the null hypothesis, alternative hypothesis for hypothesis testing for this situation.
b. Suppose the researchers obtain a sample of 110 randomly selected Nebraska state adults and find that 58 of them are living with spouses.
Assuming all the necessary conditions are satisfied, perform the hypothesis test and compute the P-value.
(To show your work: Write down which calculator you are using and what values you are entering into the calculator.)
c. Does the part b answer indicate that there is strong evidence that the percentage of adults living with spouses in Nebraska is higher than the national percentage? Briefly explain how your hypothesis testing results indicate this.
Suppose US womens’ shoe sizes are Normally distributed with a mean of size 8 and a standard deviation of approximately 1.2.
a. What percentage of US women do we expect to have a shoe size between sizes 8.5 and 10? (To show your work: Write down which calculator you are using and what values you are entering into the calculator.)
b. Find the cutoff value for the lowest 11% of US womens’ shoe sizes. (To show your work: Write down which calculator you are using and what values you are entering into the calculator.)
