A researcher knows that \"maternal attachment\" (MA) scores of 18 month old todd

Question

A researcher knows that "maternal attachment" (MA) scores of 18 month old toddlers who were breastfed is normally distributed with mu = 7.5 and sigma = 1.2. High scores indicate greater maternal attachment with the MA test: the maximum score is 10. She speculates that 18 month old toddlers who are not breastfed will differ in terms of their MA scores from those who were breastfed. With a sample of N = 20 non- breastfed toddlers, the researcher obtained the MA scores below. MA scores of non- breastfed toddlers: 8, 5, 4, 3, 7, 2, 3, 7, 9, 4, 6, 8, 2, 8, 8, 9, 6, 7, 7, 5 With alpha = 01, complete step 4 of the hypothesis testing procedure, what decision and conclusion should the researcher make? The researcher should retain H_0 and conclude toddlers who are not breastfed do not differ in terms of their MA scores from those who are breastfed The researcher should retain H_0 and conclude toddlers who are not breastfed differ in terms of their MA scores from those who are breastfed The researcher should reject H_0 and conclude that there is a positive correlation between breast feeding and maternal attachment The researcher should reject H_A and conclude toddlers who are not breastfed do not differ in terms of their MA scores from those who are breastfed The researcher should reject H_0 and conclude toddlers who are not breastfed differ in terms of their MA scores from those who are breastfed

Explanation / Answer

Solution:-

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: 1 - 2 = 0, 18 months old toddlers who are not brestfed will not differ in terms of their MA scores from those who were brestfed.
Alternative hypothesis: 1 - 2 0, 18 months old toddlers who are not brestfed will differ in terms of their MA scores from those who were brestfed.

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the z score.

t = x - / s/sqrt(n)

= (5.9 - 7.5) / 2.2113/sqrt(20)

= -1.6 / 0.4945 = -3.2356

The critical value of t0.01 at 19 degree of freedom is 2.86.

Interpret results. Since the calculated value of t is greaer than the tabulated value of t = 2.86 then we reject the null hypothesis H0.

Conclusion. The reasearcher should reject Ho and conclude that 18 months old toddlers who are not brestfed will differ in terms of their MA scores from those who were brestfed.

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