Question

Hypothesis Testing

Directions:

You will conduct your own hypothesis test. Find something you think is interesting and contains a proportion that you would like to test. You need to conduct a left, right or two-tailed hypothesis test based on whether or not you believe this statistic to be too low, too high or just plain wrong. You will need to state your hypothesis, determine the minimum necessary sample size, perform calculations, and present your results in a short paper.

Use the following websites to help you find a statistic to test - your statistic will be a proportion (i.e. percentage) where you could test friends, colleagues, etc in order to collect your data. I will hold an online session on Tuesday, July 10 where I will go over the project and answer questions (the session will be recorded for those who are unable to attend).

Online Session Link: https://us.bbcollab.com/guest/f4869e7ef56549699665ea7dbe50078e

Websites (you do not need to use one of the ones listed below, however your data needs to come from a reputable news source)

fivethirtyeight.com

https://poll.qu.edu/

https://news.gallup.com/topic/report.aspx?utm_source=link_wwwv9&utm_campaign=item_224285&utm_medium=copy

http://www.surveyusa.com/PollHistory.aspx

http://maristpoll.marist.edu/

General outline for the report:

The first page of your report needs to have a summary of the problem being studied, what you were testing and why. You should follow this with the steps you used to conduct the hypothesis test at the = 0.05 level. You must include your p-value and test statistics (this is calculated straight from StatCrunch). Also include the critical value based on the alpha = .05 level of confidence. You may need to use equation editor to complete this step. Make sure to also give an explanation of the hypothesis test and a summation of the results.

You MUST determine what the minimum necessary sample size is for this problem.

A discussion of how the results might be changed at an = 0.1, or = 0.01 level.

Whether or not you reject/fail to reject the null hypothesis discuss what may have influenced your results.

Sample Project Examples:

(Keep in mind these examples are completely made-up so that statistics that are being referenced are NOT remotely legitimate).

(1) You read in a publication that 70% of all college students are on Facebook. Your group thinks that the actual proportion is closer to 80%. Here Ho is p <=.7 and Ha is p>.7.

To determine your minimum sample size you use the formula

np(1-p) >= 10

and solve for n:

n(.7)(1-.7)>=10

.21n>=10

n>=47.6

So your minimum sample size is 48.

You then poll 48 college students. You find that you proportion is _______ - and then you run a hypothesis test and make your conclusions.

You can use any sampling technique that you see fit (yes you could create a survey from a site like surveymonkey.com or similar). I know that you will probably NOT be able to fully gather your data using simple random sampling - but you do need to discuss your data collection technique and how you might design a data collection technique IF you had all the time and necessary resources available to you.

Also know that you do not need to reject the null hypothesis in order to get an A on this assignment! You just need to address the questions included in the rubric below. Getting results that you were not expecting is awesome! Think of this project as a journey and NOT a destination.

Answer 1

Let us start with the website http://www.surveyusa.com/PollHistory.aspx and 'Results of SurveyUSA News Poll #24048' is taken up for this study. it shows that 58% of the people own their houses. Let us assume that 65% own their houses.

To determine the sample sizes, following binomial distribution (as in case of percentage data) we use the formula np(1-p) = 7

Now Null hypothesis H₀ : p <= 0.58 against alternative hythesis H1 : p > 0.58

Hence n = 7/(0.58*0.42) = 29 (approx) and accordingly np = 16.82

Using simple random sampling without replacement 29 units are selected.and their mean is obtained as 22.36

Now using z test, we can calculate the value of the test statistic = sqrt(29)*(calculated mean - np) / sqrt(7) = 5.38

z score = 1.96 at 5% level of signioficance. Hence we can conclude that the test is significant and accordingly the null hypothesis is rejected at 5% level.

If we consider 1% level, then z score is 2.58, and then also null hypothesis is rejected. But point to be noted that a test statistics which is significant at 5% level may not necesssarily be significant at 1% but the test necessarily be significant at 5% if it is significant at 1% level.