Question

36. Some people enjoy dunking cookies into their cups of tea before eating the cookie. We are going to find a sample proportion of people that are "dunkers." How large a sample size should we take to estimate the proportion to within 0.03 with 95% confidence, assuming that no previous study has been conducted?: O a. 17 Ob. 33 Oc. 545 Od. 1068 Questions 37-38: A random sample of 20 adults who have frequent headaches count the number of headaches they experience over one week. These 20 adults then get chiropractic treatment, and then they count the number of headaches they experience over the following week. A hypothesis test is to be conducted to test the following alternative hypothesis: that chiropractic treatment lowers the frequency of headaches. 37. Explain what type of test would be appropriate to conduct here.:* Oa. Paired T-Test Ob. Paired Z-Test Oc. 2 Independent Sample T-Test Od. 2 Independent Sample Z-Test Oe. Chi-Square Test for Independence 38. Explain what a Type I error would be in this context.:* O a. You decide that chiropractic treatment significantly lowers the frequency of headaches, and in fact it does. Ob. You decide that chiropractic treatment significantly lowers the frequency of headaches, and in fact it does not Oc. You decide that chiropractic treatment does not significantly lower the frequency of headaches, and in fact it does not Od. You decide that chiropractic treatment does not significantly lower the frequency of headaches, and in fact it does

Answer 1

Solution :

1. Let the sample proportion given be 0.5 since p is not given. The CI is 95% thus, we use the normal disribution with z value as 1.96

Given that the margin of error as 3% i.e 0.03

Now the estimated sample size be,

n= {Z _{$\alpha$ /2} /( margin of error )} p*(1-p)

= (1.96 / 0.03)² * 0.5 *(1-0.5)

=1067.111

Thus the estimated sample size will be 1068

Thus option d) is correct

2) Thus sample size is 20 ,we need to use exact test

Here they initially counted the headaches before treatment and then all these 20 adults are treated with chiropractic treatment. Again after the treatment they counted the number of times they experienced headache.

This is before and after case, thus we can see that, data is paired

Thus we have to use paired t test

Thus option a) is correct

3) To test whether chiropractic treatment is effective or not we need to test,

H0 : there is no difference after treatment i.e. treatment do not lower freq of headache

vs H1: there is no difference after treatment i.e. treatment lowers freq of headache

The type one error is reject H0 when it is true

This means, We rejecting the fact that treatment is not effective where in real it is not effective.

i.e we are saying treatment is effective actually its not.

Here b) you decide that chiropractic treatment significantly lowers the frequency of headache and in fact it does not

Thus option b) is correct