Question

a data set includes weights (in grams) of 38 reeses peanut butter cup miniatures. the accompanying statdisk display shows results from using all 38 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: h₁: (type integers or decimals. do not round.) identify the test statistic. (round to two decimal places as needed.) identify the p - value. round to three decimal places as needed.) state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

Explanation:

Step1: Identify null and alternative hypotheses

The claim is that the population mean \(\mu = 8.953\). So, \(H_{0}:\mu = 8.953\) and \(H_{1}:\mu
eq8.953\) (two - tailed test).

Step2: Identify test statistic

From the Statdisk display, the test statistic \(t=-3.72385\approx - 3.72\) (rounded to two decimal places).

Step3: Identify P - value

From the Statdisk display, the P - value is \(0.00065\approx0.001\) (rounded to three decimal places).

Step4: Make a decision about the null hypothesis

Since the significance level \(\alpha = 0.05\) and \(P - value=0.001<0.05\), we reject the null hypothesis \(H_{0}\).

Answer:

• \(H_{0}:\mu = 8.953\), \(H_{1}:\mu

eq8.953\)

• Test statistic: \(-3.72\)
• P - value: \(0.001\)
• Conclusion: Reject \(H_{0}\). There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean equal to \(8.953\) g.