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.]
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:
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246 |
247 |
241 |
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245 |
249 |
247 |
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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
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.
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The test statistic is more extreme than the crtitical value. |
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The p-value is smaller that the level of significance, α. |
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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.
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Marginally fail to reject the null hypothesis |
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Fail to reject the null hypothesis |
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Highly fail to reject the null hypothesis |
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Marginally reject the null hypothesis |
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Reject the null hypothesis |
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Highly reject the null hypothesis |
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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.
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It is marginally reasonable that the mean number of chocolate chips per bag is 250. |
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It is reasonable that the mean number of chocolate chips per bag is 250. |
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It is highly reasonable that the mean number of chocolate chips per bag is 250. |
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It is marginally reasonable that the mean number of chocolate chips per bag is 250. |
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It is unreasonable that the mean number of chocolate chips per bag is 250. |
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It is highly unreasonable that the mean number of chocolate chips per bag is 250. |
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No conclusion can be drawn at this time based on the findings. |
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