Math / Data & Statistics

QuestionA data set includes weights (in grams) of 32 Reese's Peanut Butter Cup Miniatures. The accompanying Statdisk display shows results from using all 32 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.
Click the icon to view the Statdisk display.
Identify the null and alternative hypotheses. $\mathrm{H}_{0}$ : $\square$ $\square$ $\square$ $\mathrm{H}_{1}$ $\square$ (Type integers or decimals. Do not round.)
Statdisk Display Cancel ``` t Test Test Statistic, t -3.79818 Criticalt: }\pm2.7440 P-value: 0.00064 ``` Print Done

Studdy Solution

STEP 1

1. The sample consists of 32 Reese's Peanut Butter Cup Miniatures.
2. The population mean is claimed to be $\mu = 8.953$ grams.
3. The significance level for the test is $\alpha = 0.01$ .
4. The test is a two-tailed t-test.

STEP 2

1. Identify the null and alternative hypotheses.
2. Analyze the Statdisk display results.
3. Make a decision based on the test statistic and critical value.
4. Conclude whether to reject or fail to reject the null hypothesis.

STEP 3

Identify the null hypothesis ( $H_0$ ) and the alternative hypothesis ( $H_1$ ).
$H_0: \mu = 8.953$
$H_1: \mu \neq 8.953$

STEP 4

Analyze the Statdisk display results.
- Test Statistic, $t = -3.79818$ - Critical t-values: $\pm 2.7440$ - P-value: $0.00064$

STEP 5

Compare the test statistic with the critical t-values and the P-value with the significance level.
- Since $-3.79818 < -2.7440$ , the test statistic falls in the critical region. - The P-value $0.00064$ is less than the significance level $\alpha = 0.01$ .

STEP 6

Make a decision.
- Since the test statistic is in the critical region and the P-value is less than $\alpha$ , we reject the null hypothesis.
Conclusion: There is sufficient evidence to reject the claim that the population mean is equal to 8.953 grams.

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Studdy Solution

STEP 1

1. The sample consists of 32 Reese's Peanut Butter Cup Miniatures.
2. The population mean is claimed to be $\mu = 8.953$ grams.
3. The significance level for the test is $\alpha = 0.01$ .
4. The test is a two-tailed t-test.

STEP 2

1. Identify the null and alternative hypotheses.
2. Analyze the Statdisk display results.
3. Make a decision based on the test statistic and critical value.
4. Conclude whether to reject or fail to reject the null hypothesis.

STEP 3

Identify the null hypothesis ( $H_0$ ) and the alternative hypothesis ( $H_1$ ).
$H_0: \mu = 8.953$
$H_1: \mu \neq 8.953$

STEP 4

Analyze the Statdisk display results.
- Test Statistic, $t = -3.79818$ - Critical t-values: $\pm 2.7440$ - P-value: $0.00064$

STEP 5

Compare the test statistic with the critical t-values and the P-value with the significance level.
- Since $-3.79818 < -2.7440$ , the test statistic falls in the critical region. - The P-value $0.00064$ is less than the significance level $\alpha = 0.01$ .

STEP 6

Make a decision.
- Since the test statistic is in the critical region and the P-value is less than $\alpha$ , we reject the null hypothesis.
Conclusion: There is sufficient evidence to reject the claim that the population mean is equal to 8.953 grams.

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Studdy Solution

STEP 1

1. The sample consists of 32 Reese's Peanut Butter Cup Miniatures.2. The population mean is claimed to be μ=8.953 \mu = 8.953 μ=8.953 grams.3. The significance level for the test is α=0.01 \alpha = 0.01 α=0.01.4. The test is a two-tailed t-test.

STEP 2

1. Identify the null and alternative hypotheses.2. Analyze the Statdisk display results.3. Make a decision based on the test statistic and critical value.4. Conclude whether to reject or fail to reject the null hypothesis.

STEP 3

Identify the null hypothesis (H0 H_0 H0​) and the alternative hypothesis (H1 H_1 H1​).H0:μ=8.953H_0: \mu = 8.953H0​:μ=8.953H1:μ≠8.953H_1: \mu \neq 8.953H1​:μ=8.953

STEP 4

Analyze the Statdisk display results.- Test Statistic, t=−3.79818 t = -3.79818 t=−3.79818 - Critical t-values: ±2.7440 \pm 2.7440 ±2.7440 - P-value: 0.00064 0.00064 0.00064

STEP 5

STEP 6

Make a decision.- Since the test statistic is in the critical region and the P-value is less than α \alpha α, we reject the null hypothesis. Conclusion: There is sufficient evidence to reject the claim that the population mean is equal to 8.953 grams.

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1. The sample consists of 32 Reese's Peanut Butter Cup Miniatures.
2. The population mean is claimed to be $\mu = 8.953$ grams.
3. The significance level for the test is $\alpha = 0.01$ .
4. The test is a two-tailed t-test.

1. Identify the null and alternative hypotheses.
2. Analyze the Statdisk display results.
3. Make a decision based on the test statistic and critical value.
4. Conclude whether to reject or fail to reject the null hypothesis.

Identify the null hypothesis ( $H_0$ ) and the alternative hypothesis ( $H_1$ ).
$H_0: \mu = 8.953$
$H_1: \mu \neq 8.953$

Analyze the Statdisk display results.
- Test Statistic, $t = -3.79818$ - Critical t-values: $\pm 2.7440$ - P-value: $0.00064$

Make a decision.
- Since the test statistic is in the critical region and the P-value is less than $\alpha$ , we reject the null hypothesis.
Conclusion: There is sufficient evidence to reject the claim that the population mean is equal to 8.953 grams.