Statistics and Probability Answers

Directions: Draw a conclusion for the given situation using the five-step hypothesis testing

procedure for population proportion in both methods (critical value method and

the p-value method)

1. A nationwide poll claims that the country’s president has a less than 64% approval rating.

In a random sample of 120 people, 69 of them gave the president a positive approval

rating. Test the claim at 0.05 level of significance.

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.

The average height of all entering freshmen students is 165 cm with the standard deviation

. To test the claim, a researcher selected a random sample of 50 freshmen of a certain

college. In this sample, and . Is the claim true?

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