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 (y = 270 min, s = 20 min). Can it be claimed that thenew blend lowers finishing times? Or is it possible that random chance alone canexplain the discrepancy? Carry out a hypothesis test of the true mean u using the 4-step procedure. Set your alpha-level to 0.05.d. What is the critical value associated with an alpha-level of 0.05?O i. -1.96O ii. -1.729iii. -1.645iv. -1.333

now will use T-DISTRIBUTION table to calculate following t-values corresponding given p-value and…

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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4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'st
A sample of 150 matched pairs of banks was formed in a study comparing banks in Turkey and Germany. Each pair contained one bank from Turkey and one from Germany. The pairings were made in such a way that the two members were as similar as possible in regard to such factors as size and age. The ratio of total loans outstanding to total assets was calculated for each of the banks. For this ratio, the sample mean difference (Turkey - Germany) was 0.0412, and the sample standard deviation of the differences was 0.3039. Test, against a two-sided alternative, the null hypothesis that the two population means are equal. (Assume a = 0.01.) Click the icon to view the critical values of the Student's t distribution. Which of the following cor greater than tn-1, a/2 O B. Ho: Hx - Hy = 0 0< 1 - *rt :H O A. Ho: Hx -Hy =0 greater than - tn - 1, a 0# 서-저 : H O D. Ho: Hx-Hy = 0 OC. Ho: Hx-Hy #0 H: Hx-Hy =0 greater than t,-1. g 05 1 - Xt :'H less than -tn-1, a O F. Ho: Hx - Hy = 0 O E. Ho: Hx -Hy =0…
4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min
Dogsled drivers, known as mushers, use several different breeds of dogs to pull their sleds. One proponent of Siberian Huskies believes that sleds pulled by Siberian Huskies are faster than sleds pulled by other breeds. He times 4040 teams of Siberian Huskies on a particular short course, and they have a mean time of 7.77.7 minutes. The mean time on the same course for 4747 teams of other breeds of sled dogs is 6.26.2 minutes. Assume that the times on this course have a population standard deviation of 1.51.5 minutes for teams of Siberian Huskies and 1.61.6 minutes for teams of other breeds of sled dogs. Let Population 1 be sleds pulled by Siberian Huskies and let Population 2 be sleds pulled by other breeds. Step 1 of 2 : Construct a 95%95% confidence interval for the true difference between the mean times on this course for teams of Siberian Huskies and teams of other breeds of sled dogs. Round the endpoints of the interval to one decimal place, if necessary.
A cell phone manufacturer tests the battery lifetimes of its cell phones by recording the time it takes for the battery charges to run out while testers are streaming videos on the phones continuously. The manufacturer claims that the population mean of the battery lifetimes of all phones of their latest model is 5.26 hours. As a researcher for a consumer information service, you want to test that claim. To do so, you select a random sample of 45 cell phones of the Español manufacturer's latest model and record their battery lifetimes. Assume it is known that the population standard deviation of the battery lifetimes for that cell phone model is 2.42 hours. Based on your sample, follow the steps below to construct a 99% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. Then state whether the confidence interval you construct contradicts the manufacturer's claim. (If necessary, consult a list of formulas.) 00 (a)…
A recent study revealed that the average weight of babies born in the United States is normally distributed with a mean of 7.5 pounds. This number is lower than recent years and so researchers are interested in determining what factors are associated with lower birth weights. One researcher decides to look at the age of the mother to determine if younger mothers have babies that are significantly heavier or lighter than average. To study this the researcher collects data from 87 babies who were born to mothers between the ages of 16 and 18. Only one baby was measured per mother. Twins and other multiple births were excluded. The average weight for these babies was 7.3 pounds with a standard deviation of .6 pounds. Was the average weight of babies of young mothers significantly different than babies in the general population? No, the difference was not significant Yes, they were lighter. Yes, they were heavier
Suppose that ten friends get together to go bowling. Also suppose that each person's score is 15 points lower for their second game than for their first game. Report the value of the correlation coefficient between game 1 score and game 2 score, with one decimal place of accuracy.
The data in the attached image represents blood pressure based on a new trial medication used in an experiment involving a total of 50 male and female subjects. There were two levels of treatment: 0 = placebo and 1 = treatment group. Family History Blood Pressure = Fam-Hist-BP; from the paternal side = PS; from the maternal side = MS; from both sides = BS; none on both sides or not known = N.; Blood pressure before the experiment = BP-Before-Exp; Blood pressure after the experiment = BP-After-Exp. Task: Construct a histogram to represent the family BP history, the subjects' BP before treatment and the subjects' BP after treatment.
According to the National Health and Nutrition Examination Survey (NHANES) sponsored by the U.S. government, a random sample of 712 males between 20 and 29 years of age and a random sample of 1,001 males over the age of 75 were chosen and the weight of each of the males were recorded (in kg). Do the data provide evidence that the younger male population weighs more (on average) than the older male population? Use “Y” for ages 20-29 and “S” for ages 75+. It was found that x̅Y=83.4, sY=18.7, x̅S=78.5, and sS=19.0. a)Suppose the test statistic is t = 2.398. What is the associated p-value? Group of answer choices 0.001 < p-value < 0.002 0.005 < p-value < 0.01 0.01 < p-value < 0.02 0.0005 < p-value < 0.001 b) Suppose the p-value is 0.02 < p-value < 0.04. At α = 0.10 what is the appropriate conclusion to make? Group of answer choices Fail to reject H0 and conclude that the mean weight of all males ages 20-29 is greater than the mean weight of all…
When does Two Related Samples occur?
5t. A magazine reports that women trust recommendations from a particular social networking site more than recommendations from any other social network platform. But does trust in this social networking site differ by gender? The following sample data show the number of women and men who stated in a recent sample that they trust recommendations made on this particular social networking site. Women Men Sample 150 170 Trust RecommendationsMade on the social networking site 111 102 (a) What is the point estimate of the proportion of women who trust recommendations made on this particular social networking site? (b) What is the point estimate of the proportion of men who trust recommendations made on this particular social networking site? (c) Provide a 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on this particular social networking site. (Round your answers to four decimal places.)
A researcher believes that among the residents of a remote community, 30% have type O blood, 50% have type A blood, 10% have type B blood and 10% have type AB blood. She takes a random sample of 80 residents and finds that 20 had type O blood, 40 had type A blood, 12 had type B blood and 8 had type AB blood. Do the data follow the hypothesized distribution of blood type for this community? Test at a = .05. Round your answers to three decimal places, if necessary. Null hypothesis: Ho: Po = 0.3, PA = 0.5, PB = 0.1, PAB = 0.1 20 40 12 8 80 80 80 80 1 1 1 20 40 8 Ho: Po = Ho: Po = Alternative hypothesis: Ho: Po = PA = PB = PAB = Ha: po # Type O 1 Ha: Po PA PB = PAB = 4 20 › PA = PA = Type 0 20 24 40 80 80 Ha: Po 0.3, PA # 0.5, PB At least one of the proportions is different. Complete the table of observed counts: Type O , PA # 0.667 Type A PB = PB = 40 Type A 40 What is the test statistic? 2.667 1 ,PB # 0 , PAB = 1 12¹ PAB Complete the table of expected counts under the null hypothesis: 12…

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