E-Text Chap 9

E-Text Chap. 9

9.54 Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more

should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10

or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance, is the true mean greater than 10? (b) Use Excel to find the right-tail p-value.

(a) At the .01 level of significance, is the true mean greater than 10?

Hypotheses: H0: μ ≤ 10

Ha: μ > 10 (claim)

Critical Value: α = 0.01, for a one-tailed test, zcrit = 2.236

Test Value: ztest = (xbar - μ) / [ s/√n ]

ztest = (14.44 - 10) / [ 4.45/√35 ]

ztest = 5.9027

Decision: ztest > zcrit  Reject the null hypothesis

Summary: There is sufficient evidence to support the claim that the true mean

is greater than 10.

(b) Use Excel to find the right-tail p-value.

The formula in Excel is: = 1 – NORMSDIST(5.9027)

The p-value returned is: 1.788 x 10-9

9.56 A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and interpret it.

(a) At the .10 level of significance, is the coin biased toward heads? Show your decision

rule and calculations.

The expected proportion of heads from a fair coin is p = 0.50

Hypotheses: H0: p ≤ 0.5

Ha: p > 0.5 (claim)

Critical Value: α = 0.10, for a one-tailed test, zcrit = 1.282

Test Value: n = 60

p = 0.5

q = 1 – p = 1 – 0.5 = 0.5

μ = np = (60)(0.5) = 30

σ = √npq = √(0.5)(0.5)(60) = 3.8730

ztest = (X - μ) / σ

ztest = (38 - 30) / 3.8730

ztest = 2.0656

Decision: ztest > zcrit  Reject the null hypothesis

Summary: There is sufficient evidence to support the claim that coin is biased

toward heads.

(b) Calculate a p-value and interpret it.

p(z > 2.0656)...