A study was performed to examine the effects of a new diet plan. Researchers measured the weight change (in kilograms) after four weeks for one group that followed the diet and another group that followed their usual eating habits. The results are provided below. Use a 0.050.05 significance level to test the claim that the two groups come from populations with the same mean weight change.Diet Group:n1=20; xˉ1=−1.8; s1=0.6n_1=20;\text{ }\bar{x}_1=-1.8;\text{ }$$s_1=0.6$$Control Group:n2=20; xˉ2=0.0; s2=0.0n_2=20;\text{ }\bar{x}_2=0.0;\text{ }$$s_2=0.0$$

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Visualizing Qualitative vs. Quantitative Data
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Frequency Distributions
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Time-Series Graph
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Mean
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Introduction to Confidence Intervals
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Determining the Minimum Sample Size Required
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Two Proportions
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Two Means - Unknown, Equal Variance
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Two Means - Unknown, Unequal Variance

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Problem 69Multiple Choice

A study was performed to examine the effects of a new diet plan. Researchers measured the weight change (in kilograms) after four weeks for one group that followed the diet and another group that followed their usual eating habits. The results are provided below. Use a $0.05$ significance level to test the claim that the two groups come from populations with the same mean weight change.
Diet Group:
$n_{1} = 20; {\overset{ˉ}{x}}_{1} = - 1.8; s_{1} = 0.6$
Control Group:
$n_{2} = 20; {\overset{ˉ}{x}}_{2} = 0.0; s_{2} = 0.0$

There is sufficient evidence to conclude that the mean weight change is different between the two groups.

There is insufficient evidence to conclude that the mean weight change is different between the two groups.

The two groups must have the same mean weight change.

A two-sample t-test must always be conducted, even when one group has no variation.

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