Math  /  Data & Statistics

QuestionSuppose the nutrition information on the package of Matilde's favorite brand of chips states that a serving size of 26 g equals about 12 chips. That means, on average, each chip should weigh 2.17 g . Matilde decides to test the accuracy of this serving size information. She plans to conduct a one-sample tt-test with a significance level of α=0.05\alpha=0.05 to test the null hypothesis, H0:μ=2.17H_{0}: \mu=2.17, against the alternative hypothesis, H1:μ2.17H_{1}: \mu \neq 2.17, where μ\mu is the average weight of a chip. Matilde selects a random sample of unbroken chips to weigh. She does not know the population standard deviation nor the distribution of chip weights, but she has confirmed that her sample does not contain any outliers. The summary statistics for her test are shown in the following table. \begin{tabular}{ccccc} Sample size & Sample mean & Sample standard deviation & Test statistic & Probability value \\ \hlinenn & xˉ\bar{x} & ss & tt & PP-value \\ 50 & 2.19 & 0.11 & 1.500 & 0.140 \end{tabular}
Based on these results, complete the following sentences to state the decision and conclusion of the test.
Matilde's decision is to \qquad the \qquad ( P=0.140P=0.140 ). There is \qquad evidence to \square the claim that the average weight

Studdy Solution
State the conclusion of the test:
There is insufficient evidence to reject the claim that the average weight of a chip is 2.17g 2.17 \, \text{g} .
Matilde's decision is to **do not reject** the **null hypothesis** (P=0.140 P = 0.140 ). There is **insufficient** evidence to **reject** the claim that the average weight of a chip is 2.17g 2.17 \, \text{g} .

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