5. The National Student Loan Survey selected a random sample of 1,280 borrowers who beganrepayment of their loans between four and six months prior to the study. The sample mean debt forundergraduate study was $18,900 and the standard deviation was about $49,000. (Note that thisdistribution is clearly skewed to the right, but because our sample size is quite large, we can rely onthe central limit theorem to assure us that the sampling distribution of the sample mean isapproximately normal.)а.Compute a 95% confidence interval for the true mean debt for all undergraduate borrowers.b. Suppose we wanted a more precise estimate, with a margin of error of just ±$2,000. How biga sample would we need to achieve this margin of error with a 95% level of confidence?

The summary of statistics is, a) Critical value: By using the z-tables, the critical value at 5%…

Answered: 5. The National Student Loan Survey…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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After numerous studies, it is estimated that the age of college students follows a normal distribution with a mean of 20.7 years and a standard deviation of 1.8 years. A random sample of 16 college students is taken and the sample mean and sample standard deviation are found to be 21.5 years and 2.3 years, respectively. a.Is the sample average of 21.5 considered an outlier (in other words, what is the chance of getting a sample mean at least as large as 21.5 assuming μ and σ are correct)? b. The calculated value of the sample standard deviation is larger than σ, is 2.3 years enough larger than 1.8 that the estimate of σ does not seem reasonable? Use probability to support your conclusion c.No matter what you got for an answer in part b, assume we no longer trust σ = 1.8 to be valid. Calculate the same probability as you did in part a, but this time, assume that σ is unknown.
Suppose that the lengths of pregnancies are normally distributed with a mean of 270 days and a standard deviation of 14 days. If a child is born in the lower 4.5% of this distribution is considered to be premature, how many days must a pregnancy last for a child to not be considered premature? (Round to the nearest day.)
1. For each day of last year, the number of vehicles passing through a certain intersection was recorded by a city engineer. One objective of this study was to determine the percentage of days that more than 425 vehicles used the intersection. If the mean data was 375 vehicles per day and the standard deviation was 25 vehicles: (f) Suppose the relative frequency distribution for the data is bell-shaped, then what is the 97.5th percentile of the distribution? 400 325 350 425
For each day of last year, the number of vehicles passing through a certain intersection was recorded by a city engineer. One objective of this study was to determine the percentage of days that more than 425 vehicles used the intersection. If the mean data was 375 vehicles per day and the standard deviation was 25 vehicles: (c) Suppose the relative frequency distribution for the data is bell-shaped, then what percentage of days between 325 and 425 vehicles used the intersection ?
A random sample of five observations from three normally distributed populations produced the following data: (You may find it useful to reference the F table.) (table is the screenshot picture) a. Calculate the grand mean. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) b. Calculate SSTR and MSTR. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) c. Calculate SSE and MSE. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) d. Specify the competing hypotheses in order to determine whether some differences exist between the population means. _H0: μA = μB = μC; HA: Not all population means are equal. _H0: μA ≤ μB ≤ μC; HA: Not all population means are equal. _H0: μA ≥ μB ≥ μC; HA: Not all population means are equal. e-1. Calculate the value of the F(df1, df2) test statistic. (Round intermediate calculations to at least 4 decimal…
Suppose the following data show the introductory interest rates on a sample of 5 credit cards: 6, 2.7, 3.3, 5.6, 3.7. Calculate the standard deviation of the sample. Note: the numbers may be different from the last problem. (please express your answer using 2 decimal places)
1.In a trial for the university athletics competition, one aims to estimate the mean chest size of the male athletes. A random sample of 70 male athletes gave rise to an average chest size of 42 inches with a standard deviation of 16 inches. What would be the distribution of the statistic that we need to estimate the mean chest size? a. It is a normal distribution with mean 42 inches and standard deviation 16 inches. b. it is a student's t distribution with degree of freedom 69. c. It is a student's t distribution with mean 42 inches and standard deviation 16 inches. d. it is a normal distribution with degree of freedom 69. 2.What is the standard error of the sample mean in problem 1? a. 1.91 b. 0.23 c. 17.5 d. 16 3.What would be the critical value if we need to find a 95% confidence interval for the true average chest size in problem 1? a. 2.29 b. 1.99 c. 1.67 d. None of the above
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2. The average gasoline price of one of the major oil companies has been $1.00 per gallon. Because of shortages in production of crude oil, it is believed that there has been a significant increase in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $1.04. Assume that the standard deviation of the population (o) is $0.12. a) State the null and the alternative hypotheses for testing the belief. b) Describe a Type I error and a Type II error for this situation. c) What is the critical value at a = .05? d) what's your What is the t-statistic or z-statistic associated with the above sample results?
A government sample survey plans to measure the total cholesterol level of an SRS of men aged 20-34.Suppose that, in fact, the total cholesterol level of all men aged 20-34 follows the Normal distribution with mean M = 182milligrams per deciliter (mg/dL.) and standard deviation G = 37 mg/dL.0 Attempt 4(a) Choose an SRS of 100 men from this population. What is the sampling distribution of &? (Use the units of my/dL.)
1. Vera Bradley, a U.S. handbag and luggage brand, recently surveyed a simple random sample of n = 320 customers who bought something from the newly launched winter collection. They would like to determine whether or not the mean age of the customers is below 35. If so, they will deliver a 2024 Spring collection catering to a younger crowd. Suppose they found that the sample mean was 34.7 years old and the population standard deviation was 4 years. What is the p-value associated with the test statistic?

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