Statistics and Probability Answers

You are given the following information of a company that produces cola fizzy drinks. The

company states that the mean caffeine content per bottle of a fizzy drink is 40 mg with a

standard deviation of 7.5 mg. The quality controller is convinced that it is lower. A sample of

30 randomly drawn bottles has a mean caffeine content of 39.2 mg. Can the quality

controller reject the claim? Conduct a hypothesis test at 0.05 level of significance.

In a recent survey, a researcher claimed that the average life expectancy of people in a certain country is 72 years. Is his claim correct if a random sample of 25 deaths from his country showed a mean of 71.2 years with standard deviation of 1.2 years? Use 99% confidence level.

Among 157 African-American men, the mean systolic blood pressure was 146 mm

Hg with a standard deviation of 27. We wish to know if on the basis of these data,

we may conclude that the mean systolic blood pressure for a population of African-

American is greater than 140.

• Setup the null and alternate hypothesis (1 mark)

• Determine the type of the test (1 mark)

• Use α=0.01, conduct the test and accept or reject the hypothesis on the basis of

the test. (Given Z_0.99=2.33) (3 marks)

The average number of homes sold by a realty company is 2 homes per day. What is the probability that exactly 3 homes will be sold in the next Sunday.( Given that e=2718)

Suppose there are three different types of cakes that are sold at Tina’s Bakery. There are 4 cheesecakes, 5 vanilla sponge cakes and 2 black forest cakes. Tom takes at random 2 of these cakes without replacement. What is the probability that he takes 2 different types of cakes upon his selection?

The claim is made that Internet shoppers spend on the average $335 per year. It is desired to test that this figure is not correct at a = 0.075. Three hundred Internet shoppers are surveyed and it is found that the sample mean = $354 and the standard deviation = $125. Find the value of the test statistic and give your conclusion. Note: critical value is +1.7805 and -1.7805.

A population consists of the numbers 5, 20, 9, 4, and 2 with sample size of 3

1. Find the t-value that the area in the right tail is 0.10 with 25 degrees of freedom.

2. Find the t-value that the area in the right tail is 0.05 with 30 degrees of freedom.

3. What is the area of the region to the left of t=1.055 with n=30?

4. What is the area of the region to the right of t = 0.687 with df =20?