Part 1: For each problem, write out the following parts. Failure to do so will result in a redo.

(a) State the population being studied.

(b) State the null hypothesis symbolically or in words.

(c) State the alternative hypothesis symbolically or in words.

(d) Identify which hypothesis is the claim.

(e) State the type of test (left-, right-, two-tailed).

(f) Describe in words what a Type I error would be in context to the problem.

1. An agricultural cooperative guarantees that the mean shelf life of a certain type of dried fruit is more than 400 days.

2. A soup maker says that the standard deviation of sodium content in one serving of soup is less than 50 mg.

3. An energy bar maker claims the variance of the number of grams of carbohydrates in one bar is less than 2.5.

Part 2: How many must our friend choose correctly before a sample of games becomes statistically significant? This problem is a continuation of the problem in the slides.

1. A friend claims that he can always pick more than a majority of college football winners among 16 chosen games. We convert this to a testable hypothesis:

H0 : p 0.5, H1 : p > 0.5 (right-tailed)

The P-values for several possible outcomes for p are given below.

p P -value

8/16 0.5000

9/16 0.3085

10/16 0.1587

11/16 0.0668

12/16 0.0228

13/16 0.0062

14/16 0.0013

15/16 0.0001

(a) If using a 10% level of significance, how many picks must your friend get correct in order to believe him?

(b) If using a 5% level of significance, how many picks must your friend get correct in order to believe him?

(c) If using a 1% level of significance, how many picks must your friend get correct in order to believe him?

Part 3: For each problem, write out the following parts. Failure to do so will result in a redo.

(a) State the population being studied.

(b) State the null hypothesis symbolically or in words.

(c) State the alternative hypothesis symbolically or in words.

(d) Identify which hypothesis is the claim.

(e) State the type of test (left-, right-, two-tailed).

(f) Determine whether to use a binomial or t-distribution.

(g) Find/calculate the P-value.

(h) Write the conclusion (in terms of support for the claim, as given in the slides).

7.1 Let X be the percentage of successful free throws made in a season and Y be the percentage of successful field goals made in a season. A sample of 6 players are drawn and the sample correlation coefficient is r = 0.784. Use a 1% level of significance to test the claim that there is no correlation between free throws and field goals.

7.2 A tourist agency in Nevada claims the mean daily cost of meals and lodging for 2 adults traveling in the state is more than $300. A consumer protection advocate wants to test this claim. In a random sample of 35 pairs of adults traveling in Nevada, the mean daily cost of meals and lodging is $316 with standard deviation $30. Is there enough evidence at 2% to support the agencys claim?

7.2 A researcher claims that the mean age of residents in a small town is more than 32 years. The ages (in years) of a random sample of 36 residents are listed below. At 1%, is there enough evidence to support the researchers claim?

41 33 47 31 26 39 19 25 23 31 39 36

41 28 33 41 44 40 30 29 46 42 53 21

29 43 46 39 35 33 42 35 43 35 24 21

Use a computer to calculate the sample mean and sample standard deviation.

7.3 In the game Yahtzee, 5 dice are rolled and points are rewarded based on the numbers that appear. Sixes is multiplying the number of 6s that appear by 6 (for example, if the rolls were 5, 3, 5, 6, 6, then sixes yields 12 points). Jethro has recieved attention recently because he claims to be able to achieve greater than 18 points each roll (meaning at least three 6s out of 5 dice). On a news channel, Jethro rolls 6, 6, 4, 6, 6 which scores 24 points! Should we be impressed? Use a 5% level of significance.