One of the most striking human accomplishments is the achievement of intelligibl
ID: 3249347 • Letter: O
Question
One of the most striking human accomplishments is the achievement of intelligible speech by age five. Males generally develop at a slower rate than females, and in a recent large study of speech development in young children, investigators hypothesized that a greater proportion of boys would have speech deficits for this reason. Random samples of healthy two-year-old males and females were followed over the course of a year, and at age 3 each child was classified as having a speech deficit or not. The data are given in the table below: a) At the .05 significant level, do the data provide evidence of the hypothesized development differences? Provide appropriate statistical evidence for your conclusion. b) Is this an observational study or an experiment? Justify your response.Explanation / Answer
Solution:-
a) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: PMale< PFemale
Alternative hypothesis: PMale > PFemale
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.1565
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.0288
z = (p1 - p2) / SE
z = 5.51
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is more than 5.51. We use the Normal Distribution Calculator to find P(z > 5.51) = Less than 0.0001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.
b) This is an observational study.
The researcher has no control over the variables in an observational study. An experiment is a method of applying treatments to a group and recording the effects. A good group experiment will have two basic elements: a control and a treatment.
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