Hypothesis testing assignment

This assignment will involve designing and implementing a brief statistical experiment, formulating a statistical hypothesis, and interpreting the results in terms of this hypothesis.

Experiment

Each person will have to come up with an idea for something to collect data on.   You should think of something you can measure or record at least 50 observations of (1) relatively easily and in a short period of time (over a day or two at most), (2) in similar/identical circumstances, (3) and something that varies in value.  You will be trying to estimate the population mean of either a continuous measurement (value) or proportion (anything with a yes/no or two-value outcome).  The measurement should be something that varies in a random fashion.  If the measurement doesn’t vary, there is nothing to test since it doesn’t change.   The measurement can be collected in a survey fashion, a designed experiment, or an observational study.  Before conducting your experiment you must specify a hypothesis test about either the population value of mu (mean) or the population proportion (p) using common sense.

Examples

Test of population mean

§  Sit in Starbucks, record the price each person pays for an order (no matter what it is).  This is an observational study because I have no control over who does what.  Hypothesis: H0: mu=$5, HA: mu ne $5.

§  Repeatedly time myself to see how many minutes I can do something for: for instance, how long I can juggle without dropping the balls, holding my breath, how long it takes me to re-sort a shuffled deck of cards.  These are all designed experiments.  If you are timing yourself, try not to look at the stopwatch until after (you may try harder the longer you go and this will make the repetitions not identical).  Also, if you do something physical like hold your breath that may make you tired after a while, try to take breaks.  Try to pick something you can’t learn to do more quickly over time or “warm up” to (like solve the same puzzle repeatedly).

§  Survey your friends about their score on their last test (fraction), how much they earn per hour, how many hours of sleep they got last night.

Test of population proportion

§  Record the sex of customers in line at Starbucks (male/female, let p=proportion of males).  H0: p=0.5, HA: p ne 0.5; record whether they ask for a receipt (p=proportion who want the receipt).  H0: p=0.2, HA: p ne 0.2.   Sit at a traffic light, record whether or not the car crosses the crosswalk when it stops at a red light.  H0: p=0.6, HA: p ne 0.6. 

§  Designed experiment: Call your dog’s name, see if dog will respond to you in 5 seconds (p=proportion of times they do).  H0: p=0.6, HA: p ne 0.6.   Shoot a basketball at a hoop from the same distance, see if score or not (p=proportion of times you score).  H0: p=0.4, HA: p ne 0.4.

§  Survey: ask your friends (or random strangers) a yes/no question that you would not know the answer to ahead of time—do you put on your left shoe on first, are you left or right handed, does your name start with a consonant or a vowel.  Make sure this is something you would get enough answers of each.

Bad examples:

§  Measure how long it takes you to shower on average (you don’t shower enough times in 2 days)

§  Measure your weight each morning (doesn’t change enough over 2 days)

§  Ask your friends if they are Democratic or Republican (here, probably most will be Democratic, or you will likely know ahead of time what they are)

§  How long it takes you to chug a beer (you couldn’t physically chug 50 beers over, say 2 days), or how long it takes you to sprint 100 meters (you would get tired doing this repeatedly, and the conditions would change)

§  Ask strangers if they smoke pot (people may not give you the honest answer)

Restrictions on choices:

§  You may not choose to do a trivial experiment like a test of proportions by flipping a coin (heads or tails) or how what proportion of rolls of a die you get an even or odd number or a specific number.  Nothing that is a trivial probability/gambling type experiment.  Be a little more creative.

§  You may do one of the experiments I mentioned above or something similar to the one I will show you.

§  Are you performing a designed experiment, observational study, or survey

§  Brief description of what you will be doing and how.   This is especially important if it is a designed experiment since you need to make sure you can ensure as much as possible identical conditions.  (Ex: I will be timing how long I can hold my breath.  I will have a friend time me using a stopwatch.  They will instruct me five seconds before timing to prepare myself and take a deep breath, and count down the seconds.  After every time, I will take a minute to relax.  We will do this in two sessions over two days.). 

§  What is the null and alternative hypothesis you will be testing.  Is it a test of proportions or population mean?  Explain in one sentence why you think this null hypothesis is valid (Ex: I have timed myself before and I know I usually can hold my breath for 30 seconds; I know the typical drink at Starbucks costs about $4.50; it seems reasonable that men and women equally visit Starbucks).

§  Do you foresee any difficulties in collecting the data?

Your final report must include the following:

Restate the above details in essay form, and

1.       Show the calculation of the test statistic.  (in our case, z=-0.28 or 9.47)

2.       Give a 95% confidence interval for population mean or proportion, in our case (0.34, 0.62) or (5.62, 5.95)

3.       Report the p-value of the test.   Say, based on 1 and 3, whether you reject or fail to reject your null hypothesis.  In our case the p-values are 0.77 and 0.  So in the first case we don’t reject, in the second we do.

4.       On the final page, paste an excel table with the data you collected and calculations.

Your writeup (essay) should not be longer than 2 pages.  The excel table will be added at the end.

A few questions to address in your writeup:

§  Did the results of your test surprise you?  How so?

§  Did you anticipate any issues in data collection?  Did any issues come up that you did not anticipate?  What would you have done differently in designing your test?   For instance, I thought it would take less time to collect my Starbucks data.  It took me over an hour.  I also thought it would be easier to hear the cashier announce the price.  I tried to avoid looking like I was listening to customers’ orders.

Technical points:

§  For proportions, you assign one response to be “success” (1) and the other “failure” (0).  You can either do this manually, or code it in Excel.  In a column next to your responses, enter a code like =IF(A2="F",1,0).  This codes female (“F”) as 1, anything else (“M”) as 0. 

§  To calculate the mean, use the formula AVERAGE.  For standard deviation, do STDEV.S.

Calculation of the statistic:  Assume you have n measurements.

Population mean

Let H0: .   Let  be the sample mean of your measurements.  Let s be the standard deviation (STDEV.S) of the measurements.

Z statistic:

The 95% confidence interval for the true value of  is

The 95% confidence rejection region is

The p-value is 2*(1-NORMDIST(ABS(zstat), 0, 1, TRUE)) in Excel

AccountingQueen

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Status NEW Posted 18 Aug 2017 05:08 AM My Price 10.00

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