Question

In: Statistics and Probability

A researcher is testing the hypothesis that baby weight (in pounds) at 6 months after birth...

A researcher is testing the hypothesis that baby weight (in pounds) at 6 months after birth is related to breastfeeding (in oz). The regression equation is Weight = 6.5 + .48 * Milk/day. The Standard Error (SE) of the slope is 0.13, and the data were gathered from a sample of 320 babies (Alpha level is set at 0.05.) Which one of the following statements is INCORRECT?

Hypothesis testing for a significant slope shows evidence that Milk/day is a statistically significant slope.

Based on this regression equation, milk intake per day positively predicts weight at 6 months.

Hypothesis testing evidence does not support the decision of rejecting the null hypothesis.

The estimated weight of a baby who has 29 oz milk per day is 20.42 pounds.

Expert Solution

The regression equation is Weight = 6.5 + .48 * Milk/day.

We want to test the hypothesis that the hypothesis that baby weight (in pounds) at 6 months after birth is related to breastfeeding (in oz).

Standard Error (SE) of the slope is 0.13

The hypothesis testing problem is:

Vs

The test statistic is:

Since the sample size n=320 the degrees of freedom is 319

The critical t value at 5% level of significance with 319 degrees of freedom is:

tcrit=1.967

Since 3.69>1.967, we reject the null hypothesis at 5% level of significance.

Therefore hypothesis testing for a significant slope shows evidence that Milk/day is a statistically significant slope.

Hence, the statement Based on this regression equation, milk intake per day positively predicts weight at 6 months is incorrect.

The estimated weight of a baby who has 29 oz milk per day is given by:

Weight = 6.5 + .48 * 29

Weight = 6.5 + 13.92

Weight = 20.42

Therefore the estimated weight of a baby who has 29 oz milk per day is 20.42 pounds.

orchestra answered 2 years ago

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