MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Suppose it was found that in a random sample of 200 individuals who were underweight (defined as having a BMI of under 18.5), 8 of them were hospitalized with COVID-19. Of a corresponding group of 400 individuals who were classified as severely obese (defined as having a BMI of at least 45.0), 32 were hospitalized with COVID-19.
(a) What is the 95% confidence interval for the difference between proportions (to 4 decimal places)?
(b) Based on your result in (a), would you reject or fail to reject the null hypothesis? Why do you conclude this?

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Suppose it was found that in a random sample of 200 individuals who were underweight (defined as having a BMI of under 18.5), 8 of them were hospitalized with COVID-19. Of a corresponding group of 400 individuals who were classified as severely obese (defined as having a BMI of at least 45.0), 32 were hospitalized with COVID-19.
(a) What is the 95% confidence interval for the difference between proportions (to 4 decimal places)?

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Suppose it was found that in a random sample of 200 individuals who were underweight (defined as having a BMI of under 18.5), 8 of them were hospitalized with COVID-19. Of a corresponding group of 400 individuals who were classified as severely obese (defined as having a BMI of at least 45.0), 32 were hospitalized with COVID-19.
(a) What is the 95% confidence interval for the difference between proportions (to 4 decimal places)?
(b) Based on your result in (f), would you reject or fail to reject the null hypothesis? Why do you conclude this?

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A researcher administers a treatment to a sample from a population with a mean of m=50. If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect, the the null hypothesis states that m=40. True or false?

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Suppose it was found that in a random sample of 200 individuals who were underweight (defined as having a BMI of under 18.5), 8 of them were hospitalized with COVID-19. Of a corresponding group of 400 individuals who were classified as severely obese (defined as having a BMI of at least 45.0), 32 were hospitalized with COVID-19.
(a) If you wanted to test this null hypothesis at the 95% confidence level, what would be your critical z?
(b) What is the standard error of the difference between proportions (to 4 decimal places)?

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To evaluate the effect of a treatment, a sample ofn = 8 is obtained from a population with a mean of m =50, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 55.
Assuming that the sample variance is s2 =32, use a
two-tailed hypothesis test with a = .05 to determine whether the treatment effect is significant and compute both Cohen’s d and r2 to measure effect size.
Assuming that the sample variance is s2 = 72, repeat the test and compute both measures of effect size.
Comparing your answers for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test and measures of effect size?

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To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 25, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M= 27.4 with SS = 64. If the sample consists of 9 individuals, what is the t statistic, and are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05?

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To evaluate the effect of a treatment, a sample of n = 8 is obtained from a population with a mean of μ = 50, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 55.
Assuming that the sample variance is s^2 = 32 , use a two-tailed hypothesis test with α = .05 to determine whether the treatment effect is significant and compute both Cohen’s d and r^2 to measure effect size.
Assuming that the sample variance is s^2 = 72 , repeat the test and compute both measures of effect size.
Comparing your answers for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test and measures of effect size?

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Suppose we took a random sample of 200 students and ask if they preferred morning, evening, or night classes. a.If 76 students preferred morning classes what is the 95% CI for the proportion of students who prefer morning classes? b. Based on this confidence interval what would be the decision to the hypothesis: H0 = .3 vs Ha ≠ .3 using alpha = .05? c.How large a sample should be taken in order to estimate the proportion to within 2%, with 99% confidence?

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Suppose that Randy is an analyst for the bicyling industry and wants to estimate the asking price of used entry-level road bikes advertised online in the southeastern part of the United States. He obtains a random sample of ?=13n=13 online advertisements of entry-level road bikes. He determines that the mean price for these 13 bikes is ?⎯⎯⎯=$681.87x¯=$681.87 and that the sample standard deviation is ?=$177.45s=$177.45. He uses this information to construct a 99% confidence interval for ?μ, the mean price of a used road bike.
What is the lower limit of this confidence interval? Please give your answer to the nearest cent.

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To evaluate the effect of a treatment, a sample of n = 8 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 35.
If the sample variance is s2 = 32, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05?
=
If the sample variance is s2 = 72, are the data suffi- cient to conclude that the treatment has a signifi- cant effect using a two-tailed test with α = .05?
=
Comparing your answer for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?
=

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A survey at a certain university found that 21 out of a random sample of 350 students had over $6,000 in credit card debt with a 90% confidence level of 0.04 to 0.08
If we would like the margin of error to be within 0.01, how large should the sample size be? ( Use P=0.5 for a conservative estimate.)

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