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A sports science group claims that due to improved training methods, professional cyclists burn a mean of less than 6000 calories during the annual Monaco Endurance Race. (This would be an improvement on the previously accepted value of 6000 calories.) A study of 20 randomly selected professional cyclists finds that the sample mean number of calories the cyclists burn during the race is 5884 with a sample standard deviation of 765 calories. Assume that the population of numbers of calories burned by professional cyclists during the race is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that u, the mean number of calories professional cyclists burn during the Monaco Endurance Race, is less than 6000. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. Ho: u = 6000 H: µ < 6000 O

A sports science group claims that due to improved training methods, professional cyclists burn a mean of less than 6000 calories during the annual Monaco Endurance Race. (This would be an improvement on the previously accepted value of 6000 calories.) A study of 20 randomly selected professional cyclists finds that the sample mean number of calories the cyclists burn during the race is 5884 with a sample standard deviation of 765 calories. Assume that the population of numbers of calories burned by professional cyclists during the race is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that u, the mean number of calories professional cyclists burn during the Monaco Endurance Race, is less than 6000. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. Ho: u = 6000 H: µ < 6000 O

MATLAB: An Introduction with Applications
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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I am not sure about part B and C I don't know how to calculate the p value help please .
**Introduction to Hypothesis Tests for the Population Mean** - **Step 1**: Enter the number of degrees of freedom. - **19** - **Step 2**: Select one-tailed or two-tailed. - **One-tailed** - **Step 3**: Enter the test statistic. (Round to 3 decimal places.) - **0.678** - **Step 4**: Shade the area represented by the p-value. - **Step 5**: Enter the p-value. (Round to 3 decimal places.) **Graph Description**: The graph is a bell curve representing a normal distribution. The x-axis is labeled with values from -3 to 3, and the peak of the curve aligns with 0. The specific point t = 0.678 is marked along the x-axis. The curve illustrates the p-value area on one side of the distribution, corresponding to a one-tailed test. **(c)** Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the sports science group. - Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6000. - Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6000. - Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to **Explanation** | **Check** © 2021 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility
Transcribed Image Text:**Introduction to Hypothesis Tests for the Population Mean** - **Step 1**: Enter the number of degrees of freedom. - **19** - **Step 2**: Select one-tailed or two-tailed. - **One-tailed** - **Step 3**: Enter the test statistic. (Round to 3 decimal places.) - **0.678** - **Step 4**: Shade the area represented by the p-value. - **Step 5**: Enter the p-value. (Round to 3 decimal places.) **Graph Description**: The graph is a bell curve representing a normal distribution. The x-axis is labeled with values from -3 to 3, and the peak of the curve aligns with 0. The specific point t = 0.678 is marked along the x-axis. The curve illustrates the p-value area on one side of the distribution, corresponding to a one-tailed test. **(c)** Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the sports science group. - Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6000. - Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6000. - Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to **Explanation** | **Check** © 2021 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility
A sports science group claims that, due to improved training methods, professional cyclists burn a mean of less than 6000 calories during the annual Monaco Endurance Race. (This would be an improvement on the previously accepted value of 6000 calories.) A study of 20 randomly selected professional cyclists finds that the sample mean number of calories the cyclists burn during the race is 5884 with a sample standard deviation of 765 calories. Assume that the population of numbers of calories burned by professional cyclists during the race is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that μ, the mean number of calories professional cyclists burn during the Monaco Endurance Race, is less than 6000. (a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) that you would use for the test. \[ H_0: \mu = 6000 \] \[ H_1: \mu < 6000 \] (b) Perform a t-test and find the p-value. Here is some information to help you with your t-test: - The value of the test statistic is given by \[ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \] - The p-value is the area under the curve to the left of the value of the test statistic. ### Student's t Distribution - **Step 1:** Enter the number of degrees of freedom: **19** - **Step 2:** Select one-tailed or two-tailed. ### Diagram The diagram represents a normal distribution curve for the t-distribution. With a peak at the center, the areas under the curve represent probability values. The tails are where the p-values are calculated for test statistic values that deviate from the mean under the null hypothesis assumption. The graph may show: - Centered peak representing mean or expected value. - Shaded tail areas which, when calculated, represent p-values for one-tailed or two-tailed tests depending on selected region. Terminology: - **\(\mu\):** Population mean. - **\(\bar{x}\):** Sample mean. - **\(s\):** Sample standard deviation. - **\(n\):** Sample size.
Transcribed Image Text:A sports science group claims that, due to improved training methods, professional cyclists burn a mean of less than 6000 calories during the annual Monaco Endurance Race. (This would be an improvement on the previously accepted value of 6000 calories.) A study of 20 randomly selected professional cyclists finds that the sample mean number of calories the cyclists burn during the race is 5884 with a sample standard deviation of 765 calories. Assume that the population of numbers of calories burned by professional cyclists during the race is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that μ, the mean number of calories professional cyclists burn during the Monaco Endurance Race, is less than 6000. (a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) that you would use for the test. \[ H_0: \mu = 6000 \] \[ H_1: \mu < 6000 \] (b) Perform a t-test and find the p-value. Here is some information to help you with your t-test: - The value of the test statistic is given by \[ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \] - The p-value is the area under the curve to the left of the value of the test statistic. ### Student's t Distribution - **Step 1:** Enter the number of degrees of freedom: **19** - **Step 2:** Select one-tailed or two-tailed. ### Diagram The diagram represents a normal distribution curve for the t-distribution. With a peak at the center, the areas under the curve represent probability values. The tails are where the p-values are calculated for test statistic values that deviate from the mean under the null hypothesis assumption. The graph may show: - Centered peak representing mean or expected value. - Shaded tail areas which, when calculated, represent p-values for one-tailed or two-tailed tests depending on selected region. Terminology: - **\(\mu\):** Population mean. - **\(\bar{x}\):** Sample mean. - **\(s\):** Sample standard deviation. - **\(n\):** Sample size.
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