**Problem 4: Analyzing Computer Usage in a College Library**A college library is considering blocking access to certain websites if they are being used excessively for recreational purposes (e.g., social media, games). For a trial, they monitored 36 randomly selected computers over one day, recording the number of minutes spent on recreational sites. The data collected showed a sample mean of 149 minutes and a standard deviation of 69 minutes.**Tasks:**a) **Calculate a 90% Confidence Interval** Determine the confidence interval for the average daily time spent on recreational sites across the library's computers.b) **Consequences of a Type I Error** Discuss what a Type I error would mean in this context. Be specific to the situation rather than simply defining a Type I error.c) **Using the Confidence Interval** Explain how the confidence interval from part (a) can inform predictions for the hypothesis test.d) **Conduct the Hypothesis Test** Perform a hypothesis test with:- Null Hypothesis (H0): μ = 120 minutes - Alternative Hypothesis (HA): μ > 120 minutes### Steps for Calculation:1. **90% Confidence Interval Calculation** - Use the sample mean (149 minutes), standard deviation (69 minutes), and sample size (n = 36) to calculate the confidence interval for the mean.2. **Type I Error Implications** - Assess what it would mean to incorrectly conclude that computers are overused for recreational sites.3. **Confidence Interval and Hypothesis Test** - Discuss how the interval estimates comparably influence the hypothesis test results.4. **Performing the Hypothesis Test** - Use relevant statistical tests (e.g., t-test) based on the sample data to determine if there is significant evidence to block the sites.

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Answered: 4. A college library decides that it…

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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In 2018, a study was conducted that stated that the average commute time to work for Kern County residents was 22.6 minutes. Suppose you were hired to determine if the average commute time is different than it was in 2018. You randomly sample 87 individuals who commute to work from Kern county and you find that their average commute time was 20.8 minutes and you find the standard deviation of commute times for those 87 individuals was 3.6 minutes. Carry out the appropriate hypothesis test at the a = 0.05 level of significance to determine if the average commute time differs from what it was in 2018.
It currently takes users a mean of 12 minutes to install the most popular computer program made by RodeTech, a software design company. After changes have been made to the program, the company executives want to know if the new mean is now different from 12 minutes so that they can change their advertising accordingly. A simple random sample of 91 new customers are asked to time how long it takes for them to install the software. The sample mean is 11.7 minutes with a standard deviation of 1.6 minutes. Perform a hypothesis test at the 0.05 level of significance to see if the mean installation time has changed. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
12) A state fish hatchery raises trout for stocking streams and lakes. The size of the fish at release time can be controlled to a fair degree by varying the rate of feeding. The target is a mean of 10 ounces; if the fish are too small, those who catch the fish aren’t happy. A random sample of 75 fish were weighed at time of release and it was determined that the mean was 9.66 ounces with a standard deviation of 0.86 ounces. Test to determine if the fish being released have a population mean less than 10 ounces at the 0.01 significance level.
2.A firm applies a skill test to applicants to fill the vacant Quality Engineer position. The company's Human Resources Manager knows that the talent exam scores of candidates applying for this position have been distributed normally with 35.8 standard deviations in the past years. A sample of “n” was taken from the candidates who applied to the position of Quality Engineer and aptitude test of these candidates The mean score was 167.5. Find and interpret the 90% confidence interval for the average of the talent exam scores of the applicants who apply for the Quality Engineering position. . (n = the last two digits of your student number. If the last two digits are zero, choose as a two-digit number) Student ID : 2016462176
Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
A new small business wants to know if its current radio advertising is effective. The owners decide to look at the mean number of customers who make a purchase in the store on days immediately following days when the radio ads are played as compared to the mean for those days following days when no radio advertisements are played. They found that for 10 days following no advertisements, the mean was 18.3 purchasing customers with a standard deviation of 1.8 customers. On 7 days following advertising, the mean was 19.4 purchasing customers with a standard deviation of 1.6 customers. Test the claim, at the 0.02 level, that the mean number of customers who make a purchase in the store is lower for days following no advertising compared to days following advertising. Assume that both populations are approximately normal and that the population variances are equal. Let days following no advertisements be Population 1 and let days following advertising be Population 2. Step 3 of 3: Draw a…
4. A fire extinguisher salesman would like to estimate the mean number of home fires started by candles each year. He obtained fire data for seven randomly selected years from the National Fire Protection Agency. His sample produced a mean of 7041 fires with a standard deviation of 1600. Create the 90% confidence interval of interest.
7. With a previous contractor, the mean time to replace a streetlight was 3.2 days. A city councilwoman thinks that the new contractor is not getting the streetlights replaced as quickly. She selects a random sample of 12 streetlight service calls for the new contractor, and obtains the following times to replacement (days). 6.2 7.1 5.4 5.5 7.5 2.6 4.3 2.9 3.7 0.7 5.6 1.7 Using a significance level of 0.01, test the councilwoman's claim. You may assume that all conditions are satisfied.
7. In one state, the mean time served in prison by convicted burglars is 18.7 months. A researcher would like to perform a hypothesis test to determine whether the mean amount of time served by convicted burglars in her hometown is different from 18.7 months. She takes a random sample of 11 such cases from court files in her home town and finds that = 21.4 months and s = 7 months. Use a 5% significance level to perform the test. Assume normally distributed population. Perform critical-value (classical) test. Be sure to identify the null and alternate hypotheses and interpret your results. a) Hypotheses: b) Test statistic: c) Critical-value: d) Hypothesis test conclusion and interpretation:
Kendra, the Human Resources manager for Moore Manufacturing wants to determine whether the employee retention rate is higher for the company's Eastern Division than it is for the Western Division. A random sample of 25 employees from Moore Manufacturing's Eastern Division (group 1) has an average time with the company of 4.8 years and a standard deviation of 1.1 years. A random sample of 23 employees from Moore Manufacturing's Western Division (group 2) has an average time with the company of 4.1 years and a standard deviation of 0.9 years. Conduct a hypothesis test at 0.02 significance. Round answers to 4 decimal places where appropriate. The Null and Alternative Hypothesis are: Ho: mew1 = mew2 and H1: mew1 > mew2. The appropriate distribution is Student's t. What is the test statistic? What is the p-value? State the appropriate conclusion based on the information.
It currently takes users a mean of 26 minutes to install the most popular computer program made by RodeTech, a software design company. After changes have been made to the program, the company executives want to know if the new mean is now different from 26 minutes so that they can change their advertising accordingly. A simple random sample of 37 new customers are asked to time how long it takes for them to install the software. The sample mean is 27.9 minutes with a standard deviation of 7.7 minutes. Perform a hypothesis test at the 0.05 level of significance to see if the mean installation time has changed. Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.
A new small business wants to know if its current radio advertising is effective. The owners decide to look at the mean number of customers who make a purchase in the store on days immediately following days when the radio ads are played as compared to the mean for those days following days when no radio advertisements are played. They found that for 13 days following no advertisements, the mean was 23.9 purchasing customers with a standard deviation of 1.9 customers. On 6 days following advertising, the mean was 24.7 purchasing customers with a standard deviation of 1.6 customers. Test the claim, at the 0.01 level, that the mean number of customers who make a purchase in the store is lower for days following no advertising compared to days following advertising. Assume that both populations are approximately normal and that the population variances are equal. Let days following no advertisements be Population 1 and let days following advertising be Population 2. Step 3 of 3: Draw a…

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