## The marginal benefit received for each gallon of gasoline

The marginal benefit received for each gallon of gasoline consumed per week for Ang, Tony, and Gianna are provided in the accompanying table.

a. On the first graph, move the points to plot an individual demand curve for each person.

b. Assuming there are only these three people in the market, create the market demand curve for gasoline on the second graph. Move each of the points of the market demand curve provided to plot the appropriate market demand according to the dataset provided.

Gallons consumed
per week Ang’s marginal benefit Tony’s marginal benefit Gianna’s marginal benefit
1 \$7 \$4 \$8
2 \$5 \$3 \$6
3 \$3 \$2 \$4
4 \$1 \$1 \$2

## An estimate from a bus company is that young adults took 4.5 Uber rides

An estimate from a bus company is that young adults took 4.5 Uber rides each year. A student randomly polls 30 young adults and finds that these young adults have taken an average of 4.5 Uber rides each year with a standard dev of 1.2 rides. i) With significan level of 0.05 , do the test claim (Ho, Ha, critical value(s), test statistic , p-value, conclusion). ii) Come up with your own confidence level that is equivalent to the significant level of 0.05. iii) find confidence interval to estimate the population means with confident level from part ii. iv) interpret the result from the confidence interval

## A researcher want to determine whether the blood pressure of Kombucha drinkers

A researcher want to determine whether the blood pressure of Kombucha drinkers is, on average, lower then the blood pressure of non-Kombucha drinkers. Independent simple random samples of 85 Kombucha drinkers and 75 non-Kombucha drinkers yielded the following sample statistics for systolic blood pressure: Kombucha drinker n1 = 85 xbar1 = 124.1 s1= 38.7 Non -Kombucha drinker n2= 75 xbar2 = 138.7 s2= 39.2. Use a significance level of 0.10 to test the claim that the mean systolic blood pressure of Kombucha drinkers is lower than the mean systolic blood pressure of non-Kombucha drinkers.

## A pharmaceutical company

A pharmaceutical company wants to test a new drugs to see whether the medication is
effective in lowering cholesterol levels. 10 are randomly selected and pretested. The subjects were placed on the drug for 3 months, after which their cholesterol levels were tested
again. The results are listed below. Test the company’s claim that the drug lowers cholesterol levels. Assume the samples are random and dependent, and the populations are
normally distributed. Use a =0.20. Subject 1-10 Before 195, 190,205,180,240,222,188,265,234
After 180,220,199,189,170,240,214,188,260,215 a) is data matched pairs of independent? b)
claim in symbolic form c) state Ho and if claim is false, then is true. d) Ha, how many tails
and indicate the tail side(s). e) critical value(s) f) test statistic ( make sure to use t or z in
h) Reject or fail to reject Ho and why? j) conclusion

## A DVDs company claims that no more than 2%

1. A DVDs company claims that no more than 2% of the DVDs are defective. In a random
sample of 738 DVDs, it is found that 5% are defective. At the 0.01 level of significance,
test the company claim that no more than 2% are defective.
(a) write the claim in symbolic form
(b) create if and then statement for the claim
(c) identify the null hypothesis, alternative hypothesis and number of tails
(d) find test statistic
(e) find p-value
(f) conclusion about the null hypothesis ( reject or fail to reject)
(g) final conclusion that addresses the original claim.

## Supposedly 5% of the people in California

1. Supposedly 5% of the people in California was African American in 2010. A political
party wants to know how much impact African American will have, so they wonder
if that percentage has changed since then. They take a random sample of 786 adults
in California and ask, among other things, their race. 113 of the people surveyed were
African American. Can the political party conclude that the African American proportion
of the population has the changed since 2010? Same questions like the previous one.
(a) write the claim in symbolic form
(b) create if and then statement for the claim
(c) identify the null hypothesis, alternative hypothesis and number of tails
(d) find test statistic
(e) find p-value
(f) conclusion about the null hypothesis ( reject or fail to reject)
(g) final conclusion that addresses the original claim.

## Women and men have bee asked if they have a friendship that has lasted

(Hypothesis testing a claim about two population proportions) Women and men have bee asked if they have a friendship that has lasted for more than 10 years. Of the 69 women sampled, 57 said yes and of the 131 men sampled, 120 said yes. Working at 5% level of significance, use the p-value method to test the claim that

a. the population proportion of women who say yes is less than that of men who say yes
b. the population proportions that say yes are different for men and women

## Week 1

We would like to find out if there is a linear relationship between the age and vocabulary. The table shows the ages (in years) of seven children and the number of words in their vocabulary.[10]

1) Find the correlation coefficient between these two variables and interpret the result.

2) Sketch a scatter plot ad find the equation of the regression line.

3) Interpret the coefficients of the regression line.

4) Use the regression line to predict the number of words in the vocabulary of a children having 5.5 years.

5) Compute the coefficent of determination and interpret the result.

6) Test for the slope of the regression line using 𝛼=0.05.

7) Based on question 5 and 6, is the regression line a good fit? Explain

## Big Tobacco Co Ltd

The price for cigarettes sold by Big Tobacco Co Ltd was 6.00 per packet in March 2018. During the month of March, the consumption of cigarettes was 1000 packets. However, the Board of Directors of Big Tobacco Co Ltd decided to increase the price by 25% during the month of April. As a manager you noted that price elasticity of demand was 0.8. As a manager Big Tobacco Co Ltd: