Suppose a developmental psychologist is interested in the effects of fluoride in
ID: 3152524 • Letter: S
Question
Suppose a developmental psychologist is interested in the effects of fluoride in water on children’s heights. She measures the heights of a random sample (N = 21) of 12-year old children who live in an area with a very high level of natural fluorides in the water. She is interested in comparing the average height of these children with the known population mean height, which she takes from published growth tables (µ = 57.5 inches for 12-year olds). The SPSS file ‘fluoride-spring2016’ gives her raw sample data. Answer the following questions. You will want to take some of your answers from SPSS.
SPSS file ‘fluoride-spring2016’
1) 64.00
2) 49.00
3) 55.00
4) 66.00
5) 72.00
6) 59.00
7) 57.00
8) 61.00
9) 62.00
10) 60.00
11) 60.00
12) 43.00
13) 68.00
14) 70.00
15) 65.00
16) 55.00
17) 56.00
18) 61.00
19) 64.00
20) 63.00
21) 59.00
a. What statistical test is appropriate here. Why?
b. What are the null and alternative hypotheses? (Make these two-tailed.)
c. Report the sample mean and the sample standard deviation.
d. What is tobt? How many degrees of freedom are there? What is tcrit ( = 0.052tail)?
e. Report the p value of tobt from SPSS.
f. What is your conclusion about H0, using = .052tail? What is the basis for your decision? In addition to stating whether the null should be rejected or not, say what that conclusion MEANS in the context of this particular situation.
g. Calculate Cohen’s d for these data and interpret the result as a small, medium, or large effect size.
h. Based on the decision about the null hypothesis, the effect size estimate, and general considerations about statistical power, what should the psychologist conclude about the heights of children who drink highly fluoridated water? Does it differ from that of children in general? Justify your answer in a few sentences.
i. If the sample of 21 children was unbiased, and the sample size was made much, much larger, what would you predict about the decision about the null hypothesis in that case? (That is, would you expect to reject the null or retain it?) Explain why or why not.
j. Imagine that the sample size got much larger (as in sub-question h), but that the sample mean and standard deviation remained unchanged. In that case, what would happen to the value of Cohen’s d?
k. Calculate the 95% confidence interval (CI) for the population mean, based on the sample.
l. Describe why it makes sense that the number 57.5 either should or should not be included in the 95% CI, based on your decision about H0. In other words, how does knowing the CI complement the result from testing the null hypothesis?
Explanation / Answer
a) we use test for single mean(t test)
b) H0: Mu=57.5 and Ha:Mu not equal to 57.5
c) From SPSS
One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
fluoride 21 60.4286 6.70501 1.46315
sample mean=60.43 and sample standard deviation=6.70
d) From SPSS
t cal=2.002
e)
P value=0.059
f)
Since P >0.05 we accept the null hupothesis.
Hence There is not sufficient evidence to reject the Ho
One-Sample Test Test Value = 57.5 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper fluoride 2.002 20 .059 2.92857 -.1235 5.9807Related Questions
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