Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $178,000. Assume the standard deviation is $44,000. Suppose you take a simple random sample of 45 graduates. **Round all answers to four decimal places if necessary.**a. What is the distribution of $X$? $X \sim N(\_\_\_\_\_, \_\_\_\_\_)$b. What is the distribution of $\bar{x}$? $\bar{x} \sim N(\_\_\_\_\_, \_\_\_\_\_)$c. For a single randomly selected graduate, find the probability that her salary is between $169,561 and $175,241.d. For a simple random sample of 45 graduates, find the probability that the average salary is between $169,561 and $175,241.e. For part d), is the assumption of normal necessary? - No- Yes[Next Question]

As per guidelines expert have to answer first question three subparts only dear student please…

Answered: usiness Weekly conducted a survey of…

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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12need help with parts A, D and E please
In looking at the results of a standardized exam, 72% of those taking the test choose the correct answer on the first question. Answer the following for 400 test takers who are to be randomly chosen. After taking the sample and administering the test, 320 of the test takers answer the first question correctly. The sample proportion is ____________________. Find the mean and variance for the distribution of sample proportions from samples of size n = 400. Mean: __________________ Variance: ___________________ The probability is ____________________ for taking another random sample of size n = 400 test takers and more than 75% of them getting the correct answer on this question.
The average final exam score for the statistics course is 82%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 90, 78, 82, 59, 67, 71, 64, 78, 67, 57, 79, 86, 66, 56 What can be concluded at the the αα = 0.05 level of significance level of significance? For this study, we should use (t-test for a population mean, z-test for a population proportion) The null and alternative hypotheses would be: H0: (symbol) (symbol) ____ H1: (symbol) (symbol) ____ The test statistic (?,t,z) = ____ (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is (symbol) αα Based on this, we should (accept, reject, fail to reject) the null hypothesis.…
5.50 Watching live television. A survey of 442 people aged 18 to 29 revealed that 30% watch live television every day.25 You take a random sample of 20 undergraduates from your university and ask them whether they watch live TV every day. If their rate matches the 30% rate: a. What is the distribution of the number of students who say they watch live television every day? b. What is the distribution of the number of students who say that they do not watch live television every day? c. What is the probability that no more than 2 of the 20 students in your sample say that they watch live television every day?
The average income in a state was $64 comma 64,000 per person per year. Suppose the standard deviation is $29 comma 29,000 and the distribution is right-skewed. Suppose we take a random sample of 100 residents of the state. Complete parts (a) and (b) below. a. What value should we expect for the sample mean? Why? b. What is the standard error for the sample mean?
Sixty-two percent of seniors attend a particular school in a school district. Assume 500 seniors within this school district are sampled. a. Can this distribution be approximated using the Normal model? Explain. b. Use the Normal approximation to estimate the probability that at least 290 senior students are enrolled at this particular school. c. Use the Normal model to estimate the probability that between 200 and 300 senior students who are sampled are enrolled at this particular school.
The average final exam score for the statistics course is 74%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 71, 72, 53, 61, 75, 55, 75, 74, 58, 50, 71, 84, 76, 53 What can be concluded at the the αα = 0.10 level of significance level of significance? The null and alternative hypotheses would be: H0: μ = ______________ H1: μ ≠ ______________ The test statistic t= ________________(please show your answer to 3 decimal places.) The p-value = _______________________ (Please show your answer to 4 decimal places.)
Is the difference between the mean annual salaries of statisticians in Region 1 and Region 2 more than $5000? To decide, you select a random sample of statisticians from each region. The results of each survey are shown to the right. At a = 0.10, what should you conclude? Region 1 X1 = $67,700 Region 2 X2 = $62,000 01 = $8825 02 = $9025 n1 = 48 n2 = 43 Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. ..... Choose the correct null and alternative hypotheses below. B. Ho: H1- H2 O C. Ho: H1 -H2 > 5000 Ha: H1 - H2 55000 O A. Ho: H1 - H2 > 5000 + 5000 Ha: H1 - H2 2 5000 Ha: H1 - H2 = 5000 O E. Ho: H1 - H2 2 5000 O D. Ho: H1 - H2 = 5000 Ha: H1 - H2 # 5000 F. Ho: µ1 - H2 5 5000 Ha: H1 - H2 > 5000 Ha: H1 - H2 В. Z
Pavan
Is the difference between the mean annual salaries of statisticians in Region 1 and Region 2 more than $4000? To decide, you select a random sample of statisticians from each region. The results of each survey are shown to the right. At a = 0.10, what should you conclude? Region 1 X1 = $67,700 01 = $8875 Region 2 X2 = $61,000 02 = $9250 n1 = 48 n2 = 44 Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. Choose the correct answer below. O A. Reject Ho. At the 10% significance level, there is sufficient evidence to support the claim that the difference between the mean annual salaries is more than $4000. O B. Fail to reject Ho. At the 10% significance level, there is sufficient evidence to support the claim that the difference between the mean annual salaries is more than $4000. OC. Reject Ho. At the 10% significance level, there is insufficient evidence to support the claim that the difference between…
A researcher records the number of dreams that 50 college freshman students recalled during the night prior to a final exam. Number of Dreams Cumulative Frequency 4 50 3 44 2 30 1 12 0 5 A. Convert this table to a percentile rank distribution. B. What is the number of dreams at the 60th percentile?

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