MATLAB: A Practical Introduction to Programming and Problem Solving
5th Edition
ISBN: 9780128163450
Author: ATTAWAY
Publisher: ELSEVIER
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Chapter 13, Problem 15E
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Could you please help me answer parts b and c. Thanks
Suppose that we have data y = (1,...,n). Each data point y; is assumed
to be generated by a distribution with the following probability density function:
P(yi | n)=3nye, y; ≥0.
The unknown parameter is >0.
(a) Write down the likelihood for n given y, and find an expression for the maximum
likelihood estimate (MLE) of n.
(b) A Gamma(a, 3) distribution is chosen as the prior distribution for 7, where a > 0
and > 0 are known. Show that the posterior distribution of n, denoted p(n | A),
is also a gamma distribution with updated parameters that you should determine.
Do the data provide compelling evidence (at α=0.05) for concluding that true average strength for the 1078 grade exceeds that for the 1064 grade? Show all your work.
Estimate the difference between true average strengths for the two grades with a 95% confidence interval for the previous problem.
Chapter 13 Solutions
MATLAB: A Practical Introduction to Programming and Problem Solving
Chapter 13, Problem 13.2PChapter 13, Problem 13.3PChapter 13, Problem 13.4PChapter 13, Problem 1EChapter 13, Problem 3EChapter 13, Problem 6EChapter 13, Problem 7EChapter 13, Problem 8EChapter 13, Problem 9EChapter 13, Problem 10E
Chapter 13, Problem 11EChapter 13, Problem 13EChapter 13, Problem 14EChapter 13, Problem 15EChapter 13, Problem 16EChapter 13, Problem 17EChapter 13, Problem 19EChapter 13, Problem 21EChapter 13, Problem 23EChapter 13, Problem 24EChapter 13, Problem 25EChapter 13, Problem 26EChapter 13, Problem 28EChapter 13, Problem 29EChapter 13, Problem 34EChapter 13, Problem 35E
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- Use Minitab and the GPA data (GPAData.xlsx) to answer the following. a) (15 points) Is there a mean difference in High School GPA and a person's GPA following their first year of college? State the relevant hypotheses and provide the p-value from the output. Include a decision and interpretation at a 10% level of significance. b) (5 points) Is the assumption of normality satisfied? Include any plots you make to check the normality assumption and comments on your observations.arrow_forwardA researcher wants to perform a hypothesis test to see if the mean salary of the faculty in private and public institutions are different. Random samples of 36 faculty from private and public institutions were selected. Salaries of the selected faculty from private and public institutions are provided to you in facultysalary.csv file. 1. Make side-by-side boxplots of the salaries for faculty in private and public institutions (In MINITAB, go to Graphs-- >Boxplot-->and explore the available options to see how to make a side-by-side boxplot of the data). 2. Comment on your observations from the side-by-side boxplot made in part 1. 3. Calculate the descriptive statistics: mean, standard deviation for the two samples and attach the MINITAB output. 4. When carrying out a hypothesis test to achieve the aforementioned goal, would you recommend using pooled variance approach or unpooled variance approach? Provide reasoning for your choice. 5. Regardless what you recommend in part 4, carry out…arrow_forwardDave Hughes owns a local restaurant. He wonders if a redesign of the menu will increase, on average, the amount customers spend when visiting his establishment. For the following scenario, pick a statistical method we discussed regarding comparing two groups that would be appropriate for analyzing the problem. a) Hughes records the mean sales the week before the change and the week after the change and then wonders whether the difference is statistically significant. [ Select ] b) Hughes randomly samples 100 people and shows both menus to each person, asking them to rate each menu from 0 (very poor) to 20 (excellent) and then wonders whether the difference is statistically significant. [ Select ] c) Hughes randomly samples 100 people and randomly separates them into two groups of 50. He asks those in group 1 to give a rating of ‘positive’ or ‘negative’ to the old menu and those in group 2 to give a rating of ‘positive’ or ‘negative’ to the new menu. He then computes the proportion of…arrow_forward
- Search A random sample of n₁ =217 people who live in a city were selected and 107 identified as a "student". A random sample of n₂ =109 people who live in a rural area were selected and 66 identified as a "student". Find the 98% confidence interval for the difference in the proportion of people that live in a city who identify as a "student" and the proportion of people that live in a rural area who identify as a "student." a. The point estimate for difference in population proportions (City group minus Rural Area group) = Round answers to 3 decimal places. -0.112 b. Fill in the blanks of the following statement. Round answers to 3 decimal places. We are 98 0% confident that the difference in population proportion of people who identified as a "student" in city and rural area falls between -0.247 0.022 0.022 and c. Select the correct conclusion based on the above confidence interval. O Since the above confidence interval gives only negative values, we have 98% confident that the…arrow_forwardCould you please provide solutions to the follwoing questions.Thanksarrow_forwardsearch A random sample of ni A random sample of n₂ "student". 217 people who live in a city were selected and 107 identified as a "student". 109 people who live in a rural area were selected and 66 identified as a Find the 98% confidence interval for the difference in the proportion of people that live in a city who identify as a "student" and the proportion of people that live in a rural area who identify as a "student." a. The point estimate for difference in population proportions (City group minus Rural Area group) = Round answers to 3 decimal places. -0.112 b. Fill in the blanks of the following statement. Round answers to 3 decimal places. We are 98 0% confident that the difference in population proportion of people who identified as a "student" in city and rural area falls between -0.247 ✔and 0.022 0.022 c. Select the correct conclusion based on the above confidence interval. Since the above confidence interval gives only negative values, we have 98% confident that the…arrow_forward
- Could you please help me answer parts b,d and e. Thanksarrow_forwardה The state of CT claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.7 years with a standard deviation of 6.2 years. Conduct a hypothesis to test the state of CT's claim. What type of test should be run? t-test of a mean Oz-test of a proportion The alternative hypothesis indicates a two-tailed test O right-tailed test O left-tailed test Calculate the p-value. (Round properly to 4 decimal places) What is the decision? O We fail to reject the claim that the average time on death row is 15 years We reject the claim that the average time on death row is 15 years Submit Question F4 F3 F2 W E 14 POS UP T DELL F5 F6 F7 F8 F9 F10 F11 711 5 dos % $ 54 Οι 6 R T Y & 7arrow_forwardDon't answer without proper knowledge of this statistics and probability question.arrow_forward
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