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# Solution of Testing of hypothesis problems using Quick Tukey test, Paired t test and independent T-test.

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1. You work for a soda company. Last year a large survey found that 50% like you diet soda. This year a spot survey of n=900 found that 54% liked the soda. The president of the company asks you if this is an improvement in market share? Do a 1 tail test with an alpha of 5%

&#61680; What is the calculated z or t? what is the critical z or t?
&#61680; Using the TDIST excel function what is the calculated P?
If Ho is u=50%, what conclusions can you make about Ho?

2. If x bar =100 and s =4.4 for a sample size of n=16. Calculate the 99% two- tail Confidence interval around X bar and the default finite population control factor ~= 1.

3. You are conducting a survey and think that around 90% support your position. How many voter do you need to survey if your margin of error is going to be less that 3%? Remember margin of error normally refers to a 2 tail confidence interval

4. If x1 =112 avg, x2=100 avg
Ho: these two averages are the same.
Alpha =5% I tail test.
Do by hand using a 2 mean t test assuming equal variance.

S1=12 S2=8
n1=8 n2=6

What is the pooled variance?
What is the pooled std?
What is the T cal?
What is the P cal?
what is the Tinv?
Do you accept of reject the Ho that the averages are the same?

5. Do a quick Tukey test for the following two data sets.

Bob: 140,155,160,170,205,220
Diane: 170,210,215,220,225,240,250,260

How many above and below points do you have?
How many ties do you have?
How many total points for the ties?
How many overall total points do you have?
What conclusions can you make at a 2 tail 5% alpha
That ho: bob and diane are equivalent bowlers

6. Paired t test

Test before and after:( very expensive promising new drug) scores 9 patients who have high cholesterol values. This is the very first test of this drug (small initial study). Ho: that taking the new drug does not affect a person's cholesterol.

before: 260, 270, 260, 250, 255, 275, 280, 270 230
after: 240, 250, 255, 250, 260, 250, 260, 260 225
what is the average delta?
what is the std of delta?
what is the t cal?
for a one tail 5% alpha what is the critical value?
For a one tail 5% alpha, what is the P cal.
do you accept of reject the Ho?