AP Stats Ch 9 Tests of Significance

Given the following information, find the z-value for the sample. (Hint: z = (x-bar - μ)/(σ/√n))
x-bar = 68, μ = 71, σ = 7.5, n = 36

• 2.40
• 3.00
• 2.78
• 6.90

An Air Force vase mess hall has received a shipment of 10,000 gallon size cams of cherries. The supplier claims that the average amount of liquid is 0.25 gallons per can. A government inspector took a random sample of 100 cans and found that the average liquid content to be 0.28 gallons per can with a standard deviation of 0.10. Does this indicate that the supplier's claim is too low? (Use a 5% level of significance)

• Do not reject H₀ (z = 3)
• Reject H₀ (z = 2.56)
• Do not reject H₀ (z = 3)
• Reject H₀ (z = 2.56)

Slab avalanches studied in Canada have an average thickness of μ = 67 cm. The ski patrol at Vail Colorado, is studying slab avalanches in their region. A random sample of 16 avalanches showed that x-bar = 61.8cm and s = 10.6 cm. Assuming the slab thickness is normally distributed, test the claim that the mean slab thickness is the Vail region is different from that in Canada with a level of significance of 1%. 

• Do not reject H₀ (z = -1.96)
• Reject H₀ (z = -1.57)
• Do not reject H₀ (z = -1.96)
• Reject H₀ (z = -1.57)

About 76% of college professors said that if they could pick a career over again, they would choose to be a professor again. A random sample of 59 college professors in Colorado showed that 47 claim they would choose college teaching again. Does this indicate the proportion of professors in Colorado who would choose the career again is greater than the national rate of 76%? Use a 1% level of significance. 

• Do not reject H₀ (z = 0.76)
• Reject H₀ (z = 1.45)
• Do not reject H₀ (z = 1.45)
• Reject H₀ (z = 0.6)

A Type I error is when: 

• We obtain the wrong test statistic
• We reject the null hypothesis when it is actually true
• We fail to reject the null hypothesis when it's actually false
• We reject the alternate hypothesis when it's actually true

A two-tailed test with n = 41 has a test statistic z = 1.56. Which is the correct p-value?

• 0.0594
• Between 0.10 and 0.15
• Between 0.050 and 0.075
• 0.1188

A left-tailed test with n = 41 has a test statistic t = 2.72. Which is the correct p-value?

• 0.0033
• Between 0.0005 and 0.005
• Between 0.010 and 0.0010
• 0.9967

Identify the correct null hypothesis:

• H₀: p = 0.50
• H₀: µ = 100
• H₀: p = 0.48
• H₀: µ = 96

We conclude "Fail to reject H₀". What could we use as our interpretation?

• The proportion of babies born male is not 0.50.
• There is not enough evidence to say that the proportion of babies born male is different from 0.50.
• There is not enough evidence to say that the proportion of babies born male is 0.50.

Find the critical value(s) for a test using the following hypotheses and a 5% significance level.

• Z* = -1.960
• Z* = -1.645
• Z* = 1.645
• |Z*|= 1.645