Questions: A data set includes weights (in grams) of 35 Reese's 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 0.01 significance level. (i) 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 (Round to two decimal places as needed.)

A data set includes weights (in grams) of 35 Reese's 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 0.01 significance level.
(i) 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
(Round to two decimal places as needed.)

Transcript text: A data set includes weights (in grams) of 35 Reese's 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 0.01 significance level. (i) Click the icon to view the Statdisk display. Identify the null and alternative hypotheses. \[ \begin{array}{l} H_{0}: \mu=8.953 \\ H_{1}: \mu \neq 8.953 \end{array} \] (Type integers or decimals. Do not round.) Identify the test statistic $\square$ (Round to two decimal places as needed.)

Solution

Solution Steps

To solve this problem, we need to perform a hypothesis test for the mean of a population. The null hypothesis $ H_0 $ states that the population mean is equal to 8.953 grams, while the alternative hypothesis $ H_1 $ states that the population mean is not equal to 8.953 grams. We will use the sample data to calculate the test statistic, which is typically a t-statistic when the population standard deviation is unknown and the sample size is small. The test statistic can be calculated using the formula for the t-statistic:

\[ t = \frac{\bar{x} - \mu}{s/\sqrt{n}} \]

where $\bar{x}$ is the sample mean, $\mu$ is the population mean under the null hypothesis, $s$ is the sample standard deviation, and $n$ is the sample size. We will then compare the calculated t-statistic to the critical t-value at a 0.01 significance level to determine whether to reject the null hypothesis.

Step 1: Identify the Null and Alternative Hypotheses

The null hypothesis ($H_0$) and the alternative hypothesis ($H_1$) are given as follows:

Null Hypothesis ($H_0$): The population mean is equal to 8.953 grams. \[ H_0: \mu = 8.953 \]
Alternative Hypothesis ($H_1$): The population mean is not equal to 8.953 grams. \[ H_1: \mu \neq 8.953 \]

Step 2: Identify the Test Statistic

The test statistic is a value calculated from the sample data that is used to determine whether to reject the null hypothesis. The test statistic for a mean is typically calculated using the formula for the t-statistic:

\[ t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}} \]

Where:

$\bar{x}$ is the sample mean.
$\mu_0$ is the population mean under the null hypothesis.
$s$ is the sample standard deviation.
$n$ is the sample size.

Since the Statdisk display is not provided here, we assume that the test statistic has been calculated and is available. The problem asks to round this value to two decimal places.