Download Hypothesis test for the mean

Hypothesis test for the mean:
For our purposes, we will be doing a T-test on the mean and an unpooled test
when testing the difference between two means.
Test for one sample mean
Judy is a ad designer who designs the newspaper ads for the Giant grocery
store. Electronic counters at the entrance total the number of people entering the
store. Before Judy was hired, the mean number of people entering every day
was 3018. Since she has started working at the Giant the management thinks
that this average has increased. A random sample of 42
business days gave an average of 3333 people entering
the store daily with a standard deviation of 287. Does this
indicate that the average number of people entering the
store every day has increased? Use an alpha of 0.01.
Stat…. Tests…T-Test
Inpt: choose data or stats according to what is available (usually you use stats)
 0 : stands for the hypothecated mean which is in your hypothesis In this case
we are testing against the previous 3018.
X bar is the sample mean of 3333
Sx is the standard deviation of 287
n: the number in your sample 42 days
 : choose the notation used in the alternative hypothesis In this case we are
looking for an increase so choose >
Calculate
We get a p value of .000000006 which is very, very slight. Therefore, we reject
the null hypothesis and conclude that the average number of people entering the
store has certainly increased.
Test for two samples
According to a survey by the Road Information Program, Ohio is the pothole
capital of the United States with an estimated 6.8 million potholes. Potholes are
caused by water seeping into cracks, freezing and swelling the pavement. A
measurement is devised to test the resistance to water. From the following data,
determine whether there is significant difference in the resistance to water for the
two types of materials. Alpha = .05
Material A
Material B
n
36
40
mean
63.8
87.2
Stat…Tests…2-SampTTest…Stats
standard deviation
16.66
35.75
X1 is 63.8 and sx1 is 16.66 and n1 is 36
X2 is 87.2 and sx2 is 35.75 and n2 is 40
Next you choose the symbol used in the alternative hypothesis. Since we are
testing for a significance difference, that is asking if they are the same or not. So,
choose the not equal option.
DO NOT pool
Calculate
You should get a p value of .00047 which means you would reject the null
hypothesis which states the two means are equal and conclude that there is a
difference in the materials.
Test for matched pair (dependent sample)
Figure Perfect, Inc. is a women's figure salon that specializes in weight-reduction
programs. Weights in pounds for a sample of clients before and after a 6-week
introductory program are as follows.
Client
1
2
3
4
5
6
Weight before
140
160
210
148
190
170
Weight after
132
158
195
152
180
164
Use an alpha of 0.05 to determine if people lost weight.
If the program works, the weights before the program began would be higher
than the weights after the program. So the null hypothesis is that the “before”
weights = the “after” weights and the alternative hypothesis is that the “before”
weights > “after” weights meaning the program was successful. Another way to
look at the alternative is that before – after >0.
Put the before weights in L1 and the after weights in L2. Go to the top of L3 and
type L1 – L2 then enter. Now do a T test on L3. mu sub 0 is 0; use L3 for the list;
the freq is 1; choose > since if the weights before the program are significantly
greater tean the after weights, the program worked.
Calculate.
The p value is .0352 which is lower that .05 so the program did help people lose
weight. So, we reject the hypothesis and conclude that there is a difference.
However, at the .01 significance level, the program did not work.