Question

Please show ALL steps clearly. Please only use technology within capabilities of TI-84 Calculator.

1. A recent study stated that if a person smoked, the average of the number of cigarettes he or she smoked was 14 per day. To test the claim, a researcher selected a random sample of 40 smokers and found the mean number of cigarettes smoked per day was 18. Assume the population standard deviation is 6. At α = .05, test the study’s claim about cigarette smoking.

2. A bag contains 6 red balls, 2 green balls, 1 blue ball, and 1 white ball. If two balls are drawn without replacement, find the probability that:

a. The first ball is red or white.

b. The first ball is red and the second ball is white.

c. The second ball is blue given the first ball is green.

Answer 1

1)

The null and alternate hypothesis are:

H0;

Ha;

The test statistic value is

The critical values are: and

Since the test statistic value does not lies between the critical values, thus it lies in the rejection region. Thus, we have sufficient evidence to reject H₀. So, we say .

2)

a)

Required probability = P(first ball is red or white) = P(first ball is red) + P(first ball is white)

b)

Required probability = P(first ball is red and second ball is white)

c)

Required probability = P(second ball is blue | first ball is green)

= P(second ball is blue and first ball is green) / P(first ball is green)

=