**Sample Hypothesis Testing Using Cereal Sugar Content**A simple random sample of 17 different cereals is obtained. The sugar content (in grams of sugar per gram of cereal) is measured for each selected cereal. These amounts have a mean of 0.292 grams and a standard deviation of 0.167 grams. We use a 0.05 significance level to test a cereal lobbyist's claim that the mean sugar content for all cereals is less than 0.31 grams.**Formulate the Null and Alternative Hypotheses**Select the correct answer:- A. $ H_0: \mu = 0.31 $ $ H_a: \mu \neq 0.31 $- B. $ H_0: \mu = 0.31 $ $ H_a: \mu > 0.31 $- C. $ H_0: \mu = 0.31 $ $ H_a: \mu < 0.31 $ ← Correct- D. $ H_0: \mu < 0.31 $ $ H_a: \mu = 0.31 $**Find the Test Statistic**Calculate the test statistic $ t $ and round to three decimal places as needed.\[ t = \_\_ \]This exercise aims to test whether the mean sugar content in cereals is statistically less than 0.31 grams based on the sample data provided. The hypothesis testing framework involves comparing the calculated test statistic to critical values derived from a t-distribution given the sample size and significance level.

Answered: Image /qna-images/answer/8b0a6b00-3858-43b2-a1d1-e07430561248.jpg

Answered: A simple random sample of 17 different…

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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A simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.8 mg and a standard deviation of 3.18 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filters?
You were told that the mean daily cost of a hotel room in downtown St. Louis is $120. You will be needing to rent a hotel room there in the near future and you want to find the best rate. You randomly select a sample of 18 hotel rooms and find that the average cost is $121.33 with a standard deviation of $18.046. At the α = 0.05 significance level, determine if there is enough evidence to reject the claim. What is the decision for this hypothesis test? You were told that the mean daily cost of a hotel room in downtown St. Louis is $120. You will be needing to rent a hotel room there in the near future and you want to find the best rate. You randomly select a sample of 18 hotel rooms and find that the average cost is $121.33 with a standard deviation of $18.046. At the α = 0.05 significance level, determine if there is enough evidence to reject the claim. What is the decision for this hypothesis test? Reject the null because the test statistic is in the critical region and the…
The mean tar content of a simple random sample of 25 unfiltered king-size cigarettes is 21.4 mg, with a standard deviation of 3 mg. The mean tar content of a simple random sample of 25 filtered 100-mm cigarettes is 13.0 mg with a standard deviation of 3.8 mg. The accompanying table shows the data. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Let population 1 be unfiltered king-size cigarettes. Complete parts (a) through (c) below. Click the icon to view the data. a. Use a 0.05 significance level to test the claim that unfiltered king-size cigarettes have a mean tar content greater than that of filtered 100-mm cigarettes. What does the result suggest about the effectiveness of cigarette filters? Identify the null and alternative hypotheses. O B. Ho: H1 =H2 O C. Ho: H1 #H2 H1: H1 =H2 O A. Ho: H1 = H2 H:H1 H2 O F. Ho: H1 = H2 H1:H1> H2 H:H1=H2 Hq: H1…
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A simple random sample of 17 different cereals is obtained, and the sugar content (in grams of sugar per gram of cereal) is measured for each cereal selected. Those amounts have a mean of 0.293 gram and a standard deviation of 0.165 gram. Use a 0.05 significance level to test the claim of a cereal lobbyist that the mean for all cereals is less than 0.31 gram. Formulate the null and alternative hypotheses. Choose the correct answer below. OA. Ho: μ = 0.31 Ha: μ>0.31 OC. Ho: μ<0.31 H₂: p=0.31 novamal O B. Ho: μ = 0.31 Ha₂: μ0.31 O D. Ho: μ= 0.31 Hg:μ <0.31
A food distribution company claims that a restaurant chain receives, on average, 26 pounds of fresh vegetables on a daily basis. The standard deviation of these shipments is known to be 4.4 pounds. The district manager of the restaurant chain decides to randomly sample 35 shipments from the company and finds a mean weight of 24.7 pounds. Test at a 3% level of significance to determine whether or not the food distribution company sends less than 26 pounds of fresh vegetables. a. Check the TWO requirements that are satisfied. The Central Limit Theorem applies. The a distribution is normal since n > 30. The a distribution is normal since the x distribution is normal. The p distribution is normal since np > 5 and nq > 5.
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