4. Researchers working for a sports drink company would like to know if a new blendif its popular sports drink can help improve marathon runners' final running time.Marathon times, Y, are known to follow a Normal distribution. Suppose that runnersusing the old blend sports drink have a mean finishing time of 300 minutes (u = 300minutes). A random sample of 20 runners was selected to use the new blend ofsports drink in a marathon, finishing with an average time of 270 minutes and astandard deviation of 20 minutes (). Can it be claimed that the new blend lowersfinishing times? Or is it possible that random chance alone can explain thediscrepancy? Carry out a hypothesis test of the true mean u using the 4-stepprocedure. Set your alpha-level to 0.05.e. Calculate the value of the test statistic. Round to two significant digits (e.g. 1.23).

Given: n= 20.0 ,x̄= 270.0 ,s= 20.0 µ= 300.0 ,significance level(∝)= 0.05 ,degree of freedom= 19.0…

Answered: 4. Researchers working for a sports…

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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Researchers are interested in the effect of pet companionship on depression in elderly adults. They randomly select 25 participants from the target population and record their depression scores before and after spending a month with a dog (a higher score indicates a higher level of depression). The researchers then compute the difference scores for each participant (difference = after before). The mean of differences is -1 and the standard deviation of differences is 2. Can the researchers conclude that there is an effect of pet companionship on depression in elderly adults? Conduct the appropriate statistical test (two-tailed) with a = .05. Select the null hypothesis for this statistical analysis. HD=0 HD = -1 =0 H1-H2 = -1
Suppose that, in 1995, the weight of 16-year old males in the United States was normally distributed with a mean of 146 lbs and standard deviation equal to 18 lbs. Suppose that Roger, a public health researcher, believes that the popularity of video and computer gaming has made teenagers less active, and predicts that 16-year old males today weigh more than 16-year old males did in 1995. To test the theory, he chooses a random sample of 50 16-year old males and records their weights. The average weight of the sample is 150 lbs. Roger uses a ?z‑test to test the hypothesis that the average weight of 16-year old males has increased. He calculates the ?z‑statistic as 1.57 standard deviations above the mean. Use this standard normal ?z‑distribution table to calculate the ?-valueP-value of this statistic. Give your answer as a decimal rounded to four places. ?-value:
An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage, is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2 inches. The statistician will determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. The statistician plans to test the hypotheses, H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks. The conditions for inference are met. The test statistic is t = 1.35 and the P-value is between 0.05 and 0.10. What conclusion should be made at the significance level, ? Reject H0. There is convincing evidence that the true mean height of all trucks is…
The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4 years and a standard deviation of 0.5 years. He then randomly selects records on 45 laptops sold in the past and finds that the mean replacement time is 3.8 years.Assuming that the laptop replacement times have a mean of 4 years and a standard deviation of 0.5 years, find the probability that 45 randomly selected laptops will have a mean replacement time of 3.8 years or less.P(M < 3.8 years) = I got .0037 before but apparenly it is wrong so I would like to know what I did wrong and the correct answer. Thank you. Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Researchers are interested in the effect of pet companionship on depression in elderly adults. They randomly select 25 participants from the target population and record their depression scores before and after spending a month with a dog (a higher score indicates a higher level of depression). The researchers then compute the difference scores for each participant (difference = after before). The mean of differences is -1 and the standard deviation of differences is 2. Can the researchers conclude that there is an effect of pet companionship on depression in elderly adults? Conduct the appropriate statistical test (two-tailed) with a = .05. The 95% Confidence Interval for the population parameter is: [-6.16, 4.16] [-3.50, 1.50] [-1.83,-.17] [-3.06, 1.06]
6. Medical researchers conducted a study to determine whether treadmill exercise could improve the walking ability of patients suffering from claudication, which is pain caused by insufficient blood flow to the muscles of the legs. A sample of 51 patients walked on a treadmill for six minutes every day. After six months, the mean distance walked in six minutes was 370 meters, with a standard deviation of 83 meters. For a control group of 41 patients who did not walk on a treadmill, the mean distance was 330 meters with a standard deviation of 84 meters. Can you conclude that the mean distance walked for patients using a treadmill differs from the mean for the controls? Let μ1 denote the mean distance walked for patients who used a treadmill. Use the =α0.01 level of significance and the TI-84 Plus calculator. please list all 6 steps of the p method clearly
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Researchers are interested in the effect of pet companionship on depression in elderly adults. They randomly select 25 participants from the target population and record their depression scores before and after spending a month with a dog (a higher score indicates a higher level of depression). The researchers then compute the difference scores for each participant (difference after before). The mean of differences is - 1 and the standard deviation of differences is 2. Can the researchers conclude that there is an effect of pet companionship on depression in elderly adults? Conduct the appropriate statistical test (two-tailed) with a = .05. Based on the information provided above, which statistical test seems most appropriate? one sample t test O z test independent samples t test O dependent samples t test
The lifetimes of a certain brand of battery are assumed to be normally distributed with a mean of 405 hours. Find the standard deviation of these battery lifetimes, if 90% of these batteries do not achieve a lifetime of 411 hours.
Suppose you are a quality control manager at a manufacturing company that produces light bulbs. The company has recently made changes to the manufacturing process, and you want to investigate whether these changes have had a significant impact on the average lifespan of the bulbs. You collect a random sample of 30 light bulbs produced under the new process and find that the sample mean lifespan is 1200 hours with a sample standard deviation of 100 hours. Additionally, you collect a random sample of 35 light bulbs produced under the old process and find that the sample mean lifespan is 1180 hours with a sample standard deviation of 90 hours. Assuming that the population standard deviations are unknown but equal, test at a 5% significance level that the average lifespan of the light bulb has changed with the new manufacturing process. NOT FOR MARKS, just a book sample question
Researchers are interested in the effect of pet companionship on depression in elderly adults. They randomly select 25 participants from the target population and record their depression scores before and after spending a month with a dog (a higher score indicates a higher level of depression). The researchers then compute the difference scores for each participant (difference after before). The mean of differences is -1 and the standard deviation of differences is 2. Can the researchers conclude that there is an effect of pet companionship on depression in elderly adults? Conduct the appropriate statistical test (two-tailed) with a = .05. Should you reject or fail to reject the null hypothesis? Reject O Fail to reject
The water consumption per week by Brampton residences is normally distributed with an average of 125 gallons of water and a standard deviation of 10 gallons. The city of Brampton claims that the average water consumed in the state of Brampton is not 125 gallons. A team of AU students draws a simple random sample of 10 residences and find the mean consumption value of 120.3 gallons. Calculate the Zc and p-value showing all the steps.

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