Question:

The research department at Cuesta College would like to investigate the performance of first generation Cuesta College students and not first generation Cuesta College students in transfer level mathematics courses. First generation students are students whose parents have not earned a four-year college degree. For their study, the research department randomly selected 50 first generation students and 60 not first generation students enrolled at Cuesta during the 2019-2020 school year and analyzed their success in completing a transfer level mathematics course. 28 of the first generation students completed a transfer level mathematics course in the specified school year and 38 of the not first generation students completed a transfer level mathematics course in the specified school year.

We would look to estimate the difference between the population proportion of all first generation Cuesta College students who completed a transfer level mathematics course and the proportion not first generation Cuesta College students who completed a transfer level mathematics course for the 2019-2020 school year.

Check the normality condition to check that the sample sizes of each sample are large enough.

Find and interpret a 95% confidence interval for the difference between the population proportion of all first generation Cuesta College students who completed a transfer level mathematics course and the proportion not first generation Cuesta College students who completed a transfer level mathematics course for the 2019-2020 school year.

Based on the interval estimate is it plausible that the two proportions are equal? If the interval doesn't suggest, that they are equal, which of the two proportions is suggested to be larger?

Assuming that sample size (normality) condition was met in 1A, use the data to test the claim that the proportion of first generation Cuesta College students who completed a transfer level mathematics course in 2019-2020 is less than the proportion of not first generation Cuesta College students who completed a transfer level mathematics course in 2019-2020 at the 5% significance level.

State the null and alternative hypothesis.

State the P-value.

State your conclusion

Problem 3: Consider a normal random variable X with mean p and standard deviation o. a) Prove the Chebyshev inequality b) Assume u = -1 and o = 1. Evaluate the following probabilities: P(X 2). (d) The Chebyshev inequality gives a bound that is less than four times P(|X | 2 1) and gives a bound that is less than four times P(|X | > 2).Name For the following word problems state if the problem requires using the Central Limit theorem or if does Not require using the Central limit theorem Circle the correct choice: 1. What is the probability of randomly selecting an adult with an IQ score less than 75? A. Requires the Central limit theorem. B. Does not require the central limit theorem. 2. If 30 cell phones are randomly selected what is the probability the cell phones will last an average of more than 23.8 months? A. Requires the Central limit theorem. B. Does not require the central limit theorem. 3. In general Marine platoons are around 50 strong, if a sample of a given platoon is taken from a population of Marines with a mean weight of 200 pounds and with standard deviation o = 10. What is the probability that the sample mean weight will be less than 196 pounds? A. Requires the Central limit theorem. B. Does not require the central limit theorem. 4. The mean age of baseball players is 27 years. Assuming the age of baseball players are normally distributed and that the average size of a baseball team is 25 players, what is the probability a baseball player is older than 30 years if the player is randomly selected. A. Requires the Central limit theorem. B. Does not require the central limit theorem. 5. Suppose that you have a sample of 81 students from a population with mean u = 500 and with standard deviation o = 108. What is the probability that the sample mean will be greater than 483. A. Requires the Central limit theorem. B. Does not require the central limit theorem. Page 1 of 1