A nutritionist wants to test whether a new meal plan leads to a change in daily calorie intake. She records the daily intake (in calories) of 3434 participants before and after following the meal plan for one month. Let the differences (After − Before) in calorie intake be recorded and signed ranks be calculated. The sum of positive ranks is 390390 and the sum of negative ranks is 168168. Use the Wilcoxon signed-rank test for 30"\u003en\u003e30n \u003e 30 to determine if there is a significant change in calorie intake at the α=0.05α = 0.05 level. Use the following formulas:T=min⁡(T+,T−)T = \min(T^+, T^-)μT=n(n+1)4,σT=n(n+1)(2n+1)24,z=T−μTσT\mu_T = \frac{n(n+1)}{4}, \quad \sigma_T = \sqrt{\frac{n(n+1)(2n+1)}{24}}, \quad z = \frac{T - \mu_T}{\sigma_T}

There is not enough evidence at α=0.05α = 0.05 to conclude that the new meal plan leads to a change in calorie intake.

There is not enough evidence at α=0.05α = 0.05 to conclude that the new meal plan reduces calorie intake.

There is enough evidence at α=0.10\alpha=0.10 to conclude that the new meal plan increases calorie intake.

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Problem 50Multiple Choice

A nutritionist wants to test whether a new meal plan leads to a change in daily calorie intake. She records the daily intake (in calories) of $34$ participants before and after following the meal plan for one month. Let the differences (After − Before) in calorie intake be recorded and signed ranks be calculated. The sum of positive ranks is $390$ and the sum of negative ranks is $168$ . Use the Wilcoxon signed-rank test for $n is greater than 30$ to determine if there is a significant change in calorie intake at the $alpha equals 0.05$ level. Use the following formulas:
$T = \min (T^{+}, T^{-})$
$μ_{T} = \frac{n (n + 1)}{4},$

There is not enough evidence at $alpha equals 0.05$ to conclude that the new meal plan leads to a change in calorie intake.

There is enough evidence at $alpha equals 0.05$ to conclude that the new meal plan leads to a significant change in calorie intake.

There is not enough evidence at $alpha equals 0.05$ to conclude that the new meal plan reduces calorie intake.

There is enough evidence at $alpha equals 0.10$ to conclude that the new meal plan increases calorie intake.

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