# Hypothesis testing and correlation coefficient

1. A normal tomato will gain an average of 2 ounces per week during the growing season. A sample of 100 tomatoes is given a special hormone to increase their growth. The average weight gain of tomatoes in the sample was 3 ounces with a standard deviation of 1 ounce. Conduct a hypothesis test to determine if the hormone increased the tomatoes' weight gain (Ho: u is unequal to 2). Assume Alpha = .01 and remember to clearly state your null and hypothesis as well as the conclusion about the average weight gain of tomatoes.

Null hypothesis: no difference in the means

Alternate hypothesis: hypothesis mean is the average weight of the tomatoes

One tail test

alpha = 0.01

P = ?

Reject null hypothesis

Ho:?

H1:?

a = .01

reject Ho if z>

With a significance level of 0.01 we get the critical value of?

2. The U.S. government recently reported that the proportion of people feeling negative about the economy was only 30%. However, a recent gallop poll by CNN/Gallup found that in a sample of 1000 people 450 of them felt negative about the economy. Conduct a hypothesis test to determine if the proportion of people

feeling negative about the economy is really 30% or not (Ho:P=3). Assume Alpha =.05 .Clearly state the null and alternate hypothesis as well as the conclusion about the proportion of people who are feeling negative about the economy.

State the hypothesis: Ho:p=o.3

Ha: p is unequal to 3

State the significance level:a>0.05

State the test statistic: since the sample size n ?

With a significance level of 0.05 we get the z critical value 1.96

3. In a sample of 1000 male doctors in the U.S found that their average salary was $160,000 per year with a standard deviation of $250,000. Another sample of 1000 female doctors in the U.S. found that their average salary was $140,000 per year with a standard deviation $150,000. Conduct a hypothesis test to determine if the average salary of male doctors is the same as the average salary of female doctors.(Ho: umale = ufemale).Assume Alpha=.05 and remember to clearly state the null and alternate hypothesis as well as the conclusion about the average salary of male doctors vs female doctors.

mean 1: 160,000

mean 2: 25,000

z test applied for one mean

p= o,00<0.05 .reject the null hypothesis is that both means are the same .Accept alternate hypothesis that means statistically different.

Ho: u= 160,00

H1: u is unequal to 250,000

a=.05

Reject Hi if z <-1.96 or z>1.96

4. The following table shows the daily high temperature and maximum market price for electricity during 7 days this last summer .Using the data in the table calculate the regression equation,including the slope and intercept terms, R squared and the SE of the regression (SE of the estimate). Based on your results ,how well does temperature explain changes in price? How are the two variables mathematically related? How might you use your regression to forecast the price for electricity?

Temp 70 Prices 45

Temp 75 Prices 48

Temp 80 Prices 42

Temp 85 Prices 55

Temp 90 Prices 63

Temp 95 Prices 94

Temp 100 Prices 105

Y=?

I know the value of a dependent or response variable is based on values of the independent or explanatory variables, but how does this relate to this problem?

5. Suppose the following table shows the number of colds 7 different people got during the typical cold season based on the number of times they washed their hands per day during the cold season.Calculate the correlation coefficient and interpret its meaning as applied to this problem.In addition, using a hypothesis test determine if the correlation coefficient is statistically different from 0 (Ho: p=0).

# of Times Wash Hands 0 #of colds 7

1 4

2 3

3 2

4 2

5 3

6 1

I know the line passes through the data points and a value of 1 indicates a linear relationship exactly but how can I relate this to this problem?

Problems 1-3 State the null and alternate hypothesis and conclusion. I have shown what I have been able to do.

Problem 4: Calculate the regression equation, including the slope and intercept terms, R squared and the SE of the regression.

Problem 5: Calculate the correlation coefficient and interpret its meaning as applied to this problem.In addition using a hypothesis test to determine if the correlation coefficient is statistically different from 0 (Ho:p=0).

#### Solution Summary

This solution involves conducting hypothesis testing, calculating regression equations, and calculating correlation coefficients.