Homework Answers

Show that the function f defined on [1,0] by f(x) = (-1)^n-1 for 1/n+1 <x< = 1/n (for n= 1,2,3,...) is integrable on [0,1]

Examine the following series for convergence: "\\sum _{n=0}^{\\infty }\\left(\\frac{n-2}{2n+3}\\right)^n"

find "\\lim _{n\\to \\infty }\\left(\\frac{1}{\\left(2n+1\\right)^2}+\\frac{2}{\\left(2n+2\\right)^2}\\frac{3}{\\left(2n+3\\right)^2}\\right)+...+\\frac{3}{25n}"

An association of City Mayors conducted a study to determine the average number of times a family went to buy necessities in a week. They found that the mean is 4 times in a week. A random sample of 20 families were asked and found a mean of 5 times in a week and a standard deviation of 2. Use 5% significance level to test that the population mean is not equal to 5. Assume that the population is normally distributed.

A garment factory distributes two brands of jeans. If it is found that 75 out of 250 customers prefer brand A and that 30 out of 150 prefer brand B, can we conclude at 0.05 level of significance that brand A outsells brand B?

A study claims that on average, male high school students spend at least 3.39 hours a day playing video games with a standard deviation of 2.05 hours. A random sample of 30 teenagers were surveyed and the results showed that these teenagers spend 4.12 hours a day playing video games.

What is the null hypothesis for the given problem?

2.1 Suppose P(A) = 0.75 and P(B) = 0.82. Find the following:

2.1.1 P (A and B) if A and B are independent. (2)

2.1.2 P (not A and not B), if A and B are independent. (2)

2.1.3 P (A and B), if A and B are mutually exclusive. (1)

2.2 Solve the following inequality. (3)

x2 - 5x + 6 ≥ 0

Conduct a traditional hypothesis test for the null hypothesis H0: µ = 100 against the alternative

hypothesis H1: µ > 100 based on the 35 random observations. The sample mean is 105 and the

sample standard deviation is 15. Use α = 0.01.