Math Answers

A random sample of 20 drinks from a soft-drink machine has an average content of 21.9 deciliters, with a standard deviation of 1.42 deciliters. At 0.05 level of significance, test the hypothesis that μ = 22. 2 against the alternative hypothesis μ < 22.2. Assume that the distribution is normal.

A researcher claims that 13% of all motorcycle helmets have manufacturing flaws that could potentially cause injury to the wearer. A sample of 150 of these helmets revealed that 18 contained such defects.

A random sample of 20 drinks from a soft-drink machine has an average content of 21.9 deciliters, with a standard deviation of 1.42 deciliters. At 0.05 level of significance, test the hypothesis that μ = 22. 2 against the alternative hypothesis μ < 22.2. Assume that the distribution is normal.

Your given ∑ 𝑥 = 44 , ∑ 𝑥2 = 174, ∑ 𝑥𝑦 = 1324, in addition you also given the values of y

as:

Y 26 28 24 18 35 24 36 25 31 37 30 32

3a. calculate the Pearson correlation coefficient [7]

3b. estimate the y value associated with x=4 [8].

3c. You are given the mean of 20.3 for a random sample of 90 observations from a normal distribution population with a standard deviation of 3.9. Construct a 95% confidence level and interpret your answer. [3]

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)

y'' - 3y' - 10y = 0 ; y(0)=1 and y'(0)=10

Identify the surfaces of the following equations by converting them into equations in the Cartesian form. Show your complete solutions. z^2=4+4r^2