Question

a data set includes weights (in grams) of 35 reeses peanut butter cup miniatures. the accompanying statdisk display shows results from using all 35 weights to test the claim that the sample is from a population with a mean equal to 8.953 g. test the given claim by using the display provided from statdisk. use a 0.05 significance level. click the icon to view the statdisk display. identify the null and alternative hypotheses. h₀: μ = 8.953 h₁: μ ≠ 8.953 (type integers or decimals. do not round.) identify the test statistic. -3.03 (round to two decimal places as needed.) identify the p - value. (round to three decimal places as needed.)

Explanation:

Step1: Determine the type of test

This is a two - tailed t - test (since the alternative hypothesis is \(H_1:\mu
eq8.953\) and the population standard deviation is unknown). The formula for the t - statistic is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\), but we are given the t - statistic \(t=- 3.03\).
For a two - tailed t - test with \(n = 35\) (degrees of freedom \(df=n - 1=35 - 1 = 34\)).

Step2: Calculate the P - value

Using the t - distribution table or a statistical software (since we know the t - value and degrees of freedom). For a two - tailed test with \(t=-3.03\) and \(df = 34\).
We can use the property that for a t - distribution, \(P(|T|>|t|)\) gives the P - value. Looking up in the t - table or using a calculator (e.g., in R: \(2*(1 - pt(3.03,34))\)), we find that \(P - value\approx0.005\)

Answer:

\(0.005\)