A researcher investigates whether there is an association between the incidence of colds and the amount of Vitamin C taken. The study involves 96 volunteers divided into three groups: 27 take 500 mg of Vitamin C, 18 take 1000 mg, and the remainder take no Vitamin C. By the end of the study, it is found that 34 volunteers did not experience any colds, with the distribution as follows: 15 in the 500 mg group, 11 in the 1000 mg group, and the rest with no Vitamin C.### Hypothesis Testing**Null Hypothesis (H₀):** There is not an association between the incidence of colds and the amount of Vitamin C taken.**Alternative Hypothesis (Hₐ):** There is an association between the incidence of colds and the amount of Vitamin C taken.### Expected Counts TableTo test the hypothesis, a table of expected counts under the null hypothesis is completed:| | At least one cold | No colds ||----------------------|-------------------|------------|| **No Vitamin C** | 32.938 | 18.063 || **500mg Vitamin C** | 17.438 | 9.563 || **1000mg Vitamin C** | 11.625 | 11.625 |### Statistical TestingThe critical value for this test at a significance level of α = 0.10 is 4.605. To proceed, find the p-value using these expected counts, and compare it to the critical value to determine if the null hypothesis can be rejected. This setup is useful for illustrating the process of hypothesis testing and expected counts calculation in a categorical study context.

Answered: Image /qna-images/answer/6184a4e7-642a-432d-85bd-d9e44efb8c29.jpg

Answered: that 34 of the volunteers did not have…

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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Consider the following hypothesis test: H0: 4 = 15 Ha: H# 15 A sample of 50 provided a sample mean of 14.28. The population standard deviation is 7. a. Compute the value of the test statistic (to 2 decimals). (1f answer is negative, use minus "." sign.) -1.02 b. What is the p-value (to 4 decimals)? 0.3077 c. Using a = .05, can it be concluded that the population mean is not equal to 157 No Answer the next three questions using the critical value approach. d. Using a = .05, what are the critical values for the test statistic (to 2 decimals)? 1.96 e. State the rejection rule: Reject Ho if z is less than the lower critical value and is greater than the upper critical value. f. Can it be concluded that the population mean is not equal to 157 No
Some people say that more babies are born in September than in any other month. To test this claim, you take a random sample of 150 students at your school and find that 21 of them were born in September. You are interested in whether the proportion born in September is greater than 1/12-what you would expect if September was no different from any other month. Thus, the null hypothesis is Ho: p=1/12 . The P-value for your test is 0.0056. Which of the following statements correctly interprets the P-value? Assuming that the proportion of babies born in September is greater than any other month, there is a 0.0056 probability of getting a sample proportion of 21/150 or greater by chance alone. Assuming that the proportion of babies born in September is the same as any other month, there is a 0.0056 probability of getting a sample proportion of 21/150 or greater by chance alone. The probability that the proportion of September birthdays is not equal to 1/12 is 0.0056. The probability that…
Two separate samples are selected from the same population. Each have an n=8. Both samples receive a different treatment. After the treatment, the first sample has SS=16 and the second sample has SS=24. With a mean of 3 for the first group and mean of 6 for the second group, compute the t statistic. State the conclusion of these findings.
16% of all Americans suffer from sleep apnea. A researcher suspects that a different percentage of those who live in the inner city have sleep apnea. Of the 337 people from the inner city surveyed, 47 of them suffered from sleep apnea. What can be concluded at the level of significance of α= 0.05? a. The test statistic= (please show your answer to 3 decimal places.) b. The p-value = (Please show your answer to 4 decimal places.)
A law enforcement agent believes that 80% of the drivers stopped on Saturday nights for speeding are under the influence of alcohol. Suspecting that the proportion under the influence may be higher than 80%, a SRS of 140 drivers who were stopped for speeding on a Saturday night was taken. 119 of the drivers in the sample were under the influence of alcohol. The correct set of hypotheses is Group of answer choices Ho: p = 0.80 vs Ha: p = 0.85 Ho: p = 0.80 vs Ha: p > 0.80
. A sample mean, sample standard deviation, and sample size are given. Use the one-mean t-test to perform the required hypothesis test about the mean, μ, of the population from which the sample was drawn. Use the critical-value approach. Sample mean = 3.12 s = 0.59 n = 9 α = 0.01 H0: µ = 2.85 H1: µ > 2.85 The test statistics is (Round to three decimal places)
Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. Net weights actually vary slightly from bag to bag and are Normally distributed with mean u. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised, so he intends to test the hypotheses Ho: μ = 14, Ha: μ < 14. To do this, he selects 16 bags of this brand at random and determines the net weight of each. He finds the sample mean to be x = 13.88 and the sample standard deviation to be s = 0.24. Suppose in a similar test of 16 bags of these tortilla chips the P-value is 0.001. Further suppose that a is chosen to be 0.001. In that case, we would conclude that: Othere is not significant evidence that the mean net weight of the bags of chips is less than the advertised 14 oz. O there is not significant evidence that the mean net weight of the bags of chips is not less than the advertised 14 oz. O there is significant evidence that the…
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test? Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. Determine the critical region using a one-tailed test with alpha = .05. Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). Based on your analysis, is there a relationship between the drug and attention span?
Suppose you are interested in testing whether average monthly gasoline expenditure differs from $50 at the 5% significance level. You take a sample of 30 and calculate a sample mean of 51 and sample standard deviation of 12. Given this information the null and alternative hypotheses are as follows: H0: μ=50 H1: μ≠50 What is the conclusion of this test?
If you chose the α level of .01, then which of the following p value will allow you to conclude that your result is statistically significant? a. 0.005 b. 0.05 c. 0.10 d. 0.03
Suppose that you're running the following hypothesis test with a = 0.05 : H,:u= 2.00 H:u#2.00 a. If the population standard deviation is assumed to be 1.5, and a SRS of 25 observations yielded X = 2.57, then calculate the value of the test statistic that you would use to run this test. b. Determine the P-Value for the test statistic in part (a). c. Using the P-Value you calculated in part (b) state the Decision that you make about the null hypothesis. JUSTIFY YOUR DECISION.

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