A store sells bags of candy that weigh exactly 2lb, according to their packaging. Elena, the store manager tests the claim by hypothesizing that the population mean weight of the bags is not equal to 2lb. She randomly selects 15 bags and found that the sample mean weight is 1.9968lb with a standard deviation of 0.0286lb. Assuming the weights of the bags are normally distributed, the test statistic t for a hypothesis test of H0:μ=2 versus Ha:μ≠2 is t≈−0.43 with 14degrees of freedom. If p-value>0.20 and the level of significance is α=0.05, which of the following statements are accurate for this hypothesis test to evaluate the claim that the true population mean weight of the bags is significantly not equal to 2lb?Select all that apply: A) Reject the null hypothesis that the true population mean weight of the bags is equal to 2lb. B) Fail to reject the null hypothesis that the true population mean weight of the bags is equal to 2lb. C) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean weight of the bags is not equal to 2lb. D) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean weight of the bags is not equal to 2lb.

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Asked Jun 13, 2019
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A store sells bags of candy that weigh exactly 2lb, according to their packaging. Elena, the store manager tests the claim by hypothesizing that the population mean weight of the bags is not equal to 2lb. She randomly selects 15 bags and found that the sample mean weight is 1.9968lb with a standard deviation of 0.0286lb. Assuming the weights of the bags are normally distributed, the test statistic t for a hypothesis test of H0:μ=2 versus Ha:μ≠2 is t≈−0.43 with 14degrees of freedom. If p-value>0.20 and the level of significance is α=0.05, which of the following statements are accurate for this hypothesis test to evaluate the claim that the true population mean weight of the bags is significantly not equal to 2lb?

Select all that apply:
 
A) Reject the null hypothesis that the true population mean weight of the bags is equal to 2lb.
 
B) Fail to reject the null hypothesis that the true population mean weight of the bags is equal to 2lb.
 
C) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean weight of the bags is not equal to 2lb.
 
D) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean weight of the bags is not equal to 2lb.
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Expert Answer

Step 1

It is given that the store sells bags of weight, exactly 2lb. The claim is that the population mean weight of the bags is not equal to 2lb. For a sample of 15 bags, it was found that the sample mean weight is 1.9968lb with a standard deviation of 0.0286lb.

The hypotheses for the test are,

H0: µ = 2 versus Ha: µ ≠ 2.

The test statistic value is –0.43 with 14 degrees of freedom.

The significance level α = 0.05 and p-value is greater than 0.20.

Step 2

Decision rule based on p-value:

At level of significance α, if the p-value ≤ α, then reject the null hypothesis, H0. Otherwise fail to reject H0.

If H0 is rejected, then it can be interpreted that “there is enough evidence to suggest that H0 is false, that is, to support the claim made by the alternate hypothesis, Ha at level of significance α”.

Step 3

Decision for the test based on p-value:

Here, the significance level α = 0.05 and p-value is greater than 0.20.

Thus, the p-value is not less than or equal to the level of significance, α = 0.05. Therefore, by decision rule, do not reject the null hypothesis.

Thus, the conclusion is, ‘Fail to reject the null hypothesis that the true popu...

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