PROBLEM The house brand premium chocolate chip cookie for Sale Mart Supermarket is called Choco-Champs. The company sells them only in a small pack, claiming in advertisements that this sized package of cookies is figuratively bursting with about 250 real chocolate chips contained within the cookies. A consumer testing lab tech is double checking this claim, and has collected a random sample of 9 packs of Choco-Champs from as many randomly selected store locations. A technician appropriately cold washes the cookies and counts the chips in each package. The results of these cold washes were recorded as follows: 246247241245249247243245251 Test the claim by Sale Mart with the equivalence of 99% confidence. [HINTS: When calculating sample statistics, round any answers to the nearest whole chip, if necessary. You should round any probability distribution values, standardized scores and/or any probabilities to the nearest thousandth, if necessary though without reporting any insignificant digits.] 14.) What is the absolute value of the critical value, rounded to the thousandths place? In other words, ignore any positive or negative signs. 15.) What is the p-value that corresponds with the test statistic value, expressed as a decimal rounded to the nearest thousandth? 16.) Compute the lower and upper bounds for the 99% confidence interval associated with this sample mean and sample size.Express your answer rounded to the nearest thousandth if necessary.lower or left bound:uppor or right bound: 17.) Check all of the following rejection rules that apply to this hypothesis testing context. The test statistic is more extreme than the crtitical value. The p-value is smaller that the level of significance, α. The hypothesized value falls outside the corresponding confidence interval. 18. What is the most appropriate technical conclusion, based on the available evidence (e.g., the given sample size) and testing at the reported level of significance? NOTES: For a marginal finding, let's agree the difference between test stat and critical value is approximately 0.2 or less. For an extreme (high) finding, let's agree the test stat is approximately double or half the critical value. Marginally fail to reject the null hypothesis Fail to reject the null hypothesis Highly fail to reject the null hypothesis Marginally reject the null hypothesis Reject the null hypothesis Highly reject the null hypothesis No conclusion can be drawn at this time based on the findings. 19. What is the most appropriate contextual conclusion, based on the available evidence (e.g., the given sample size) and testing at the reported level of significance? This states the findings without statistical jargon. It is marginally reasonable that the mean number of chocolate chips per bag is 250. It is reasonable that the mean number of chocolate chips per bag is 250. It is highly reasonable that the mean number of chocolate chips per bag is 250. It is marginally reasonable that the mean number of chocolate chips per bag is 250. It is unreasonable that the mean number of chocolate chips per bag is 250. It is highly unreasonable that the mean number of chocolate chips per bag is 250. No conclusion can be drawn at this time based on the findings.

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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PROBLEM

The house brand premium chocolate chip cookie for Sale Mart Supermarket is called Choco-Champs. The company sells them only in a small pack, claiming in advertisements that this sized package of cookies is figuratively bursting with about 250 real chocolate chips contained within the cookies. A consumer testing lab tech is double checking this claim, and has collected a random sample of 9 packs of Choco-Champs from as many randomly selected store locations. A technician appropriately cold washes the cookies and counts the chips in each package. The results of these cold washes were recorded as follows:

246	247	241
245	249	247
243	245	251

Test the claim by Sale Mart with the equivalence of 99% confidence. [HINTS: When calculating sample statistics, round any answers to the nearest whole chip, if necessary. You should round any probability distribution values, standardized scores and/or any probabilities to the nearest thousandth, if necessary though without reporting any insignificant digits.]

14.) What is the absolute value of the critical value, rounded to the thousandths place? In other words, ignore any positive or negative signs.

15.) What is the p-value that corresponds with the test statistic value, expressed as a decimal rounded to the nearest thousandth?

16.) Compute the lower and upper bounds for the 99% confidence interval associated with this sample mean and sample size.

Express your answer rounded to the nearest thousandth if necessary.

lower or left bound:

uppor or right bound:

17.) Check all of the following rejection rules that apply to this hypothesis testing context.

		The test statistic is more extreme than the crtitical value.
		The p-value is smaller that the level of significance, α.
		The hypothesized value falls outside the corresponding confidence interval.

18. What is the most appropriate technical conclusion, based on the available evidence (e.g., the given sample size) and testing at the reported level of significance? NOTES: For a marginal finding, let's agree the difference between test stat and critical value is approximately 0.2 or less. For an extreme (high) finding, let's agree the test stat is approximately double or half the critical value.

		Marginally fail to reject the null hypothesis
		Fail to reject the null hypothesis
		Highly fail to reject the null hypothesis
		Marginally reject the null hypothesis
		Reject the null hypothesis
		Highly reject the null hypothesis
		No conclusion can be drawn at this time based on the findings.

19. What is the most appropriate contextual conclusion, based on the available evidence (e.g., the given sample size) and testing at the reported level of significance? This states the findings without statistical jargon.

		It is marginally reasonable that the mean number of chocolate chips per bag is 250.
		It is reasonable that the mean number of chocolate chips per bag is 250.
		It is highly reasonable that the mean number of chocolate chips per bag is 250.
		It is marginally reasonable that the mean number of chocolate chips per bag is 250.
		It is unreasonable that the mean number of chocolate chips per bag is 250.
		It is highly unreasonable that the mean number of chocolate chips per bag is 250.
		No conclusion can be drawn at this time based on the findings.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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