Question

2. A leading consumer magazine, The False Traders, claims that the small coffee sold at PHILZ coffee shop does not contain 12 ounces of coffee. A sample of 25 customers who purchased a small coffee yielded the following information:

- a sample mean of 12.10 ounces and a sample standard deviation of 0.25 ounces.

(5)        a. Set up a 95% confidence interval for the true population mean.

(10)      b. At the 10% level, test the alternate hypothesis that the true mean is not equal to 12 ounces.

3. The table below lists pitches in a baseball game for two pitchers and the breakdown of “strikes” and “balls” (good pitches and bad pitches). The summary statistics are also listed.

Pitcher	Strikes	Balls	Total
Bumgarner	76	32	108
Cueto	76	41	117

  Bumgarner                  Cueto

            Sample Mean (pitches per inning) 12.0                              13.0

            Sample Variance (pitches per inning) 3.5 8

            Sample Size (# of innings) 9 9

             (an “inning” is one of the rounds in a game)

(5)        a. At the 99% level, test the alternate hypothesis that Cueto throws more pitches per inning than Bumgarner for the entire season (population of pitches):

(5)        b. Set up a 90% confidence interval for the true difference in the proportion of Balls thrown by each pitcher for the entire season:

(5)        c. Perform a hypothesis test to see if the proportion of throwing strikes for Bumgarner and Cueto is not equal for the entire season. Set the Type I error equal to 10%.

Answer 1

a)

Xbar +- t * s/sqrt(n)

b)

t-value based Population MEAN Hypothesis Test
	xbar = sample mean =	12.1
	s = sample standard deviation =	0.25
	n = sample size =	25
	α = alpha =	0.1
Step 1: State Ho and Ha
	Population parameter comparison value?			12
	Is this a LEFT, RIGHT or TWO tailed test?			TWO-tailed
	Null Hypothesis:	Ho: µ = 12
	Alternate Hypothesis:	Ha: µ ≠ 12
Step 2: State Decision Criteria; Find Critical Values
	Reject Ho if t < -1.711 or t > 1.711
	or Reject Ho if p-value < α = 0.1
Step 3: Calculate Test Statistic
	Test statistic = t =	2
	p-value =	0.05693985
Step 4: Make Decision
	Reject Ho
	Reject Ho since p-value (0.0569) IS less than α, alpha, =    0.1.
	Also, Reject Ho since the Test statistic (2) meets the rejection criteria in STEP 2.
Step 5: Summarize Decision
	There is sufficient statistical evidence to reject Ho.

Please give me a thumbs-up if this helps you out. Thank you! :)