Consider the example from the previous problem, in part (b). The sizes (in grams) of Latavia's 14 oranges are 124, 126, 129, 130, 134, 136, 139, 142, 146, 149, 152, 154, 155, and 157 g. a. Find the sample mean of Latavia's data. b. Make a boxplot or a histogram of Latavia's data with a bin size of 10. c. If even a small sample is graphed and has no major skew or outliers, it is generally reasonable to assume that the population "could reasonably be normal," and therefore that the sampling distribution of the mean is approximately normal. This is the "normal population" condition. Does this sample appear to satisfy this condition? d. Latavia reads online that medium-sized navel oranges have a mean mass of 131 g with a standard deviation of 18 g. She is interested to test if the Fresh Foods oranges match those parameters, State a null and alternative hypothesis for this situation using symbols. Note that Latavia is making two assumptions in her test. e. Calculate a test statistic: what is the z-score of Latavia's mean within the sampling distribution if the provided values hold? Use the formulas for the mean and standard deviation of the sampling distribution found last class (see Math Notes box in this lesson). f. Calculate her p-value, the probability of Latavia getting a sample mean as extreme as the one she got if the online data is correct. Sketch and shade a standard normal curve to represent the p-value. Can Latavia reject the hypothesis at a = 0.05? g. What can Latavia conclude about the oranges at Fresh Foods? h. What kind of error, Type I or Type II, might Latavia have made? Describe the effects of such an error in context.
Consider the example from the previous problem, in part (b). The sizes (in grams) of Latavia's 14 oranges are 124, 126, 129, 130, 134, 136, 139, 142, 146, 149, 152, 154, 155, and 157 g. a. Find the sample mean of Latavia's data. b. Make a boxplot or a histogram of Latavia's data with a bin size of 10. c. If even a small sample is graphed and has no major skew or outliers, it is generally reasonable to assume that the population "could reasonably be normal," and therefore that the sampling distribution of the mean is approximately normal. This is the "normal population" condition. Does this sample appear to satisfy this condition? d. Latavia reads online that medium-sized navel oranges have a mean mass of 131 g with a standard deviation of 18 g. She is interested to test if the Fresh Foods oranges match those parameters, State a null and alternative hypothesis for this situation using symbols. Note that Latavia is making two assumptions in her test. e. Calculate a test statistic: what is the z-score of Latavia's mean within the sampling distribution if the provided values hold? Use the formulas for the mean and standard deviation of the sampling distribution found last class (see Math Notes box in this lesson). f. Calculate her p-value, the probability of Latavia getting a sample mean as extreme as the one she got if the online data is correct. Sketch and shade a standard normal curve to represent the p-value. Can Latavia reject the hypothesis at a = 0.05? g. What can Latavia conclude about the oranges at Fresh Foods? h. What kind of error, Type I or Type II, might Latavia have made? Describe the effects of such an error in context.
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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Transcribed Image Text:Consider the example from the previous problem, in part (b). The sizes (in grams) of Latavia's 14 oranges are
124, 126, 129, 130, 134, 136, 139, 142, 146, 149, 152, 154, 155, and 157 g.
a. Find the sample mean of Latavia's data.
b. Make a boxplot or a histogram of Latavia's data with a bin size of 10.
c. If even a small sample is graphed and has no major skew or outliers, it is generally reasonable to assume that the population “could
reasonably be normal," and therefore that the sampling distribution of the mean is approximately normal. This is the "normal
population" condition. Does this sample appear to satisfy this condition?
d. Latavia reads online that medium-sized navel oranges have a mean mass of 131 g with a standard deviation of 18 g. She is
interested to test if the Fresh Foods oranges match those parameters. State a null and alternative hypothesis for this situation using
symbols. Note that Latavia is making two assumptions in her test.
e. Calculate a test statistic: what is the z-score of Latavia's mean within the sampling distribution if the provided values hold? Use
the formulas for the mean and standard deviation of the sampling distribution found last class (see Math Notes box in this lesson).
f. Calculate her p-value, the probability of Latavia getting a sample mean as extreme as the one she got if the online data is correct.
Sketch and shade a standard normal curve to represent the p-value. Can Latavia reject the hypothesis at a = 0.05?
g. What can Latavia conclude about the oranges at Fresh Foods?
h. What kind of error, Type I or Type II, might Latavia have made? Describe the effects of such an error in context.
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