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 = 58.0 inches for 12-year olds). The data file ‘fluoride-spring2020.csv’ gives her raw sample data. Answer the following questions. You will want to take some of your answers from spss.

Spps file data:

60
54
65
62
59
57
52
69
61
63
66
62
50
70
66
53
66
63
65
59
49

. (3 pts) If the sample of 21 children was unbiased, and the sample size was made much larger and remained unbiased, what would you predict about the decision about the null hypothesis in that case? (That is, would you expect to reject the null or fail to reject it?) Explain why or why not.

J. (2 pts) 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. (3 pts) Calculate the 95% confidence interval (CI) for estimating the population mean, based on the sample. (Do this by hand; the option to find the CI in JASP is for the difference between the two means, not the estimate of the population mean based on the sample data.)   

L. (2 pts) Describe why it makes sense that the number 58.0 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?

Answer 1

If the sample of 21 children was unbiased, and the sample size was made much larger and remained unbiased, what would you predict about the decision about the null hypothesis in that case? (That is, would you expect to reject the null or fail to reject it?) Explain why or why not.

The p-value obtained in that case when the sample size is much larger will be very less and thus, we have to reject the null hypothesis.

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?

Cohen's d is impacted by only mean difference and the standard deviation. Therefore, the sample size would have no effect on Cohen's d.

Calculate the 95% confidence interval (CI) for estimating the population mean, based on the sample. (Do this by hand; the option to find the CI in JASP is for the difference between the two means, not the estimate of the population mean based on the sample data.)   

The 95% confidence interval (CI) for estimating the population means, based on the sample is between 57.753 and 63.295.

60.524	mean Data
6.088	std. dev.
1.328	std. error
21	n
20	df
57.753	confidence interval 95.% lower
63.295	confidence interval 95.% upper
2.771	margin of error

Describe why it makes sense that the number 58.0 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?

Since 58.0 is in the confidence interval, we cannot reject Ho.

Please give me a thumbs-up if this helps you out. Thank you!