A nutritionist believes that the mean daily calorie intake is higher for athletes than for non-athletes. In a sample of 1616 athletes, the mean intake is 3,1503,150 calories with a standard deviation of 410410. In a sample of 2020 non-athletes, the mean intake is 2,9002,900 calories with a standard deviation of 350350. At α=0.05 α = 0.05 , is there enough evidence to support the nutritionist's belief? Assume population variances are not equal.

Yes, there is enough evidence at α=0.05\alpha = 0.05 to support the nutritionist’s belief.

Yes, because the mean difference is exactly 250250 calories.

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1. Intro to Stats and Collecting Data(0)

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Visualizing Qualitative vs. Quantitative Data
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Frequency Distributions
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Mean
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Two Proportions
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Two Means - Unknown, Unequal Variance
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Two Means - Unknown, Unequal Variance

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Problem 46Multiple Choice

A nutritionist believes that the mean daily calorie intake is higher for athletes than for non-athletes. In a sample of $16$ athletes, the mean intake is $3 comma 150$ calories with a standard deviation of $410$ . In a sample of $20$ non-athletes, the mean intake is $2 comma 900$ calories with a standard deviation of $350$ . At $alpha equals 0.05$ , is there enough evidence to support the nutritionist's belief? Assume population variances are not equal.

No, because the test statistic is less than the critical value.

Yes, there is enough evidence at $alpha equals 0.05$ to support the nutritionist’s belief.

No, because the sample sizes are too small to make a conclusion.

Yes, because the mean difference is exactly $250$ calories.

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