**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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For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 29 students, and the distribution of total study hours per week is bell-shaped with a mean of 14 hours and a standard deviation of 2.7 hours.Use the Empirical Rule to answer the following questions.a) 68% of the students spend between hours and hours on Statistics each week.b) 95% of the students spend between hours and hours on Statistics each week.c) 99.7% of the students spend between hours and hours on Statistics each week.
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.
5. The Instagram handle @getfollowers claims that they can increase the number of followers someone has on Instagram. In March 2015 the mean number of followers for a US teen was 150, so a random sample of 12 US teens with 150 followers was taken. The following is the number of followers, which is normally distributed, these US teens had after they paid @getfollowers for their help. Using a 0.01 level of significance, determine whether @getfollowers is effective at increasing the number of Instagram followers. 160 200 152 150 145 151 162 158 156 149 154 170 Null and Alternative Hypothesis
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
7) A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that their new tires' life expectancy has increased. In order to test the legitimacy of their advertising campaign, an independent testing agency tested a sample of 85 of their tires. The agency found the mean of the 85 tires to be 27,000 miles and the standard deviation to be 3,970 miles. Use a 0.01 level of significance and test to determine whether the company is using legitimate advertising. (Show all seven steps.)
For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 22 students, and the distribution of total study hours per week is bell-shaped with a mean of 12 hours and a standard deviation of 2.6 hours. Use the Empirical Rule to answer the following questions. a) 68% of the students spend between hours and hours on Statistics each week. b) 95% of the students spend between hours and hours on Statistics each week. c) 99.7% of the students spend between hours and hours on Statistics each week. Check Answer 100% 69°F Cloudy
34. A study was conducted to determine whether an expectant mother’s cigarette smoking has an effect on the bone mineral content of her otherwise healthy child. Particularly it was thought that smoking might lower the bone mineral content. To test this group 1 consisted of a sample of 77 newborns whose mothers smoked during pregnancy, their mean bone mineral content = 0.098 and the standard deviation = 0.026. Group 2 consisted of a sample of 161 infants whose mothers did not smoke during pregnancy, their mean = 0.095 and the standard deviation = 0.025. %3D %3D a) b) Are the two samples of data paired or independent? State the null and alternative hypothesis. (Do not do the test) buent Todousic a
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:
8. In late 2020, a poll was conducted to determine the proportion of American adults that subscribed to a TV or movie streaming service since January 2020. The surveyors randomly selected 2200 American adults. The results are shown in the relative frequency table below. Response Frequency Subscribed to at least one 794 Did not subscribe to a new one 1406 Given this information, we want to create a 95% confidence interval to estimate the proportion of American adults that subscribed to a TV or movie streaming service since January 2020. a. What is the value of the point estimate for our 95% confidence interval? b. What is the margin of error for our 95% confidence interval? (Use the formula to compute it). Round your answer to three decimal places. C. Using your answers to parts (a) and (b), find a 95% confidence interval estimating the proportion of American adults that subscribed to a TV or movie streaming service since January 2020.
There are two samples. One is a group of 8 athletes who practice and the other is a group of 5 athletes who do not practice. The mean for group 1 is 92.4 and the standard deviation is 5.83. For group 2, the mean is 81.3 and the standard deviation 7.85. the coach thinks the true mean for the athletes who did not practice is more that 8 points smaller than those who did practice. a) make the null and alternative hypotheses. calculate the test statistic and give an explanation as to why you chose this test statistic.
For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 30 students, and the distribution of total study hours per week is bell-shaped with a mean of 14 hours and a standard deviation of 2.7 hours. Use the Empirical Rule to answer the following questions. a) 68% of the students spend between hours and hours on Statistics each week. b) 95% of the students spend between hours and hours on Statistics each week. c) 99.7% of the students spend between hours and hours on Statistics each week.

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