### Hypothesis Testing for Dependent Random SamplesThe two data sets in the table below are dependent random samples. The population of \( (x - y) \) differences is approximately normally distributed. A claim is made that the mean difference \( (x - y) \) is less than 29.3.| x | 61 | 71 | 58 | 48 | 44 | 48 | 66 ||----|----|----|----|----|----|----|----|| y | 38 | 41 | 43 | 32 | 30 | 29 | 33 |For each part below, enter **only** a numeric value in the answer box. For example, do not type "z =" or "t =" before your answers. Round each of your answers to **3 places after the decimal point**.#### (a) Calculate the value of the test statistic used in this test.**Test statistic's value =** -2.760#### (b) Use your calculator to find the P-value of this test.**P-value =** 0.0164#### (c) Use your calculator to find the critical value(s) used to test this claim at the 0.07 significance level. If there are two critical values, then list them both with a comma between them.**Critical value(s) =** -1.700#### (d) What is the correct conclusion of this hypothesis test at the 0.07 significance level?- There is sufficient evidence to **support** the claim that the mean difference is less than 29.3.- There is not sufficient evidence to warrant **rejection** the claim that the mean difference is less than 29.3.- There is sufficient evidence to warrant **rejection** the claim that the mean difference is less than 29.3.- There is not sufficient evidence to **support** the claim that the mean difference is less than 29.3. ⬅️ (selected)**Note:** The conclusion selected is "There is not sufficient evidence to support the claim that the mean difference is less than 29.3."---This content aligns with educational standards and helps students understand the process of conducting hypothesis tests for dependent random samples, calculating test statistics, finding P-values, determining critical values, and drawing conclusions based on a given significance level.

Given that Mean difference (x - y) is 29.3 First three subparts already solve.

Answered: (d) What is the correct conclusion of…

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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Most soft drink beverages are packaged and sold in 12-ounce cans. You want to test to see how accurate the companies package these cans, so you take a sample of Coke cans and a sample of Pepsi cans and measure the amount of soda in each can. You wish to test the claim that the mean amount of liquid in Coke cans is less than the mean amount of liquid in Pepsi cans at a significance level of a = 0.05. a) Choose the correct null and alternative hypotheses. Ho: 12 Ha:μι>με O Ho: 1-2 Ha: 1*2 O Ho: 122 Ha:μι<μ2 Both populations are normally distributed, with cans of Coke having a population standard deviation of 0.065 and cans of Pepsi having a population standard deviations of 0.071. Your sample of 52 cans of Coke gave a mean of 12.01 ounces, while your sample of 51 cans of Pepsi gave a mean of 12.1 ounces. b) What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = c) What is the p-value for this sample? (Report answer accurate to four…
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If the significance level is α = 2% and p-value = 0.007, what is the conclusion? fail to reject the null hypothesis reject the alternate hypothesis reject the null hypothesis fail to reject the alternate hypothesis
Advertising aimed at teenagers tends to contain dance-beat music, adventure, and a fast pace rather than words. To test to see how teenagers respond to different types of commercials, 150 teenagers then watched a set of commercials with dance-beat music, adventure, and a fast pace. After the commercials, the teenagers were asked whether they would want to buy the product and 102 responded that they would buy the product. Another sample of 125 teenagers where shown a set of commercialscomprised primarily of words. After the commercials, the teenagers were asked whether they would buy the product and 60 responded that they would like to buy the product. Based on both samples, at the 5% level of significance, test the hypothesis that there is at least a 10% difference in the proportion of teenagers who would buy the product after watching the different types of commercials?
Select the correct answer below: We should reject the null hypothesis because to
Delta Flights: According to the Bureau of Transportation Statistics, 77.4% of Delta Airline’s flights arrived on time in 2010. The company is trying to improve on-time arrivals. They test the hypotheses H0: p = 0.774 versus Ha: p > 0.774. They calculate a P‑value of 0.03. Using a significance level of 0.05, which of the following is the best explanation for how to use the P‑value to reach a conclusion in this case? Since the P‑value is less than the significance level, we reject the null hypothesis. Since the P‑value is less than the significance level, we fail to reject the null hypothesis. Since the P‑value is less than the significance level, we accept the null hypothesis.
R1
A data set includes data from 400 random tornadoes. The display from technology available below results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.6 miles. Use a 0.05 significance level. Use the display to identify the ull and alternative hypotheses, test statistic, and P-value. State the final conclusion that addresses the original claim. Hypothesis test results: p. Mean of variable Ho p=2.6 HA H 2.6 Variable Sample Mean Length Std, Err. 2.75311 0.274284 399 0.558217 DF P-value 0 2885 T-Stat OA. Reject Ho. There is not sufficient evidence to support the claim that the mean tornado length is greater than 26 miles. O B. Reject Ho. There is sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles Fail to reject Ho. There is sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles C. D.Fail to reject Hn. There is not sufficient evidence to support the…
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Need Help with test statistic and p-value
A food company claims a population mean of 625 calories in their frozen lasagna entrées. A sample of 50 of these entrees were collected for a hypothesis test. The null hypothesis is that the population mean calories is 625. The alternative hypothesis is that the population mean calories is higher than 625. Below are the test results. At the 5% significance level, what is the conclusion of the test? There is not enough evidence to conclude the population mean number of calories in the entrees is more than 625. There is enough evidence to conclude the population mean number of calories in the entrees is more than 625. The mean is 630. The mean is 625.

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