Question

The objective of a study was to see whether a recorded phone would be more effective than a mailed flyer in getting voters to support a certain candidate. The study assumes a significance level of α = 0.05.

The hypotheses are:

H0: p(voted to support candidate with flyer) – p(voted to support candidate with recorded phone call) = 0, and

HA: p(voted to support candidate with flyer) – p(voted to support candidate with recorded phone call) > 0.

(a) Explain what the p-value (0.027) indicates with respect to the observed sample statistic (and other, more extreme values of that statistic). Name the sample statistic involved as well as the p-value, and use the appropriate mathematical notation. (1-2 sentences.)

(b) Write a specific statement about your interpretation of the null hypothesis, given the p-value and the specified level of significance. Be sure to cite the p-value. Does the sample evidence available support the idea that phone calls are more effective than flyers? Explain.

(c) In the conclusion for (a) & (b), which type of error are we possibly making: Type I or Type II? Explain what this error means in this context.

(d) What if the p-value for the statistical test were actually 0.18 (and not 0.027)? Explain what the p-value (0.18) indicates with respect to the observed sample statistic (and other, more extreme values of that statistic). Name the sample statistic involved, report the p-value, and use the appropriate mathematical notation. (1-2 sentences.)

(e) Write a specific statement about your interpretation of the null hypothesis, given the p-value from (d), 0.18, and the specified level of significance. Be sure to cite the p-value and α. Does the sample evidence available support the idea that phone calls are more effective than flyers? Explain.

(f) In the conclusion from (e), which type of error are we possibly making: Type I or Type II? Describe what this error means in this context.

Answer 1

p = 0.027

The P value is defined as the probability under the assumption of no effect or no difference (null hypothesis), of obtaining a result equal to or more extreme than what was actually observed. The P stands for probability and measures how likely it is that any observed difference between groups is due to chance.

b) Since, p = 0.027 < α = 0.05, null is rejected

No, the sample evidence available does not support the idea that phone calls are more effective than flyers as null is rejected.

c) Type 1 error

In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis

So, error might be that the sample evidence available support the idea that phone calls are more effective than flyers but we rejected it.

d)

p = 0.18

The P value is defined as the probability under the assumption of no effect or no difference (null hypothesis), of obtaining a result equal to or more extreme than what was actually observed. The P stands for probability and measures how likely it is that any observed difference between groups is due to chance.

e) Since, p = 0.18 > α = 0.05, null is not rejected

Yes, the sample evidence available support the idea that phone calls are more effective than flyers as null is not rejected.

f) type 2

So, error might be that the sample evidence available support the idea that phone calls are not more effective than flyers but we accepted it.