Test 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

2) 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

3) You plan to perform a hypothesis test with a level of significance of 0.05. What’s the effect on the probability of committing a Type I error if the sample size is increased?

• The probability of committing a Type I error decreases
• The probability of committing a Type I error is unchanged
• The effect cannot be determined without knowing the relevant standard deviation
• The effect cannot be determined without knowing if a Type II error is committed

4) 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 Ho (z=3)
• Reject Ho (z=2.56)
• Do not reject Ho (z=3)
• Reject Ho (z=2.56)

5. 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 Ho (z=-1.96)
• Reject Ho (z=-1.57)
• Do not reject Ho (z=-1.96)
• Reject Ho (z=-1.57)

6. 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

7. 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 Ho (z=0.76)
• Reject Ho (z=1.45)
• Do not reject Ho (z=1.45)
• Reject Ho (z=0.6)

8. What is the probability of mistakenly failing to reject a false Ho when a hypothesis test is being conducted at the 5% significance level (at 0.05)?

• 0.025
• 0.05
• 0.10
• There is insufficient information to answer this question

9. Choosing a smaller level of significance, that is a smaller alpha risk, results in:

• A lower risk of Type II error and lower power
• A lower risk of Type II error and higher power
• A higher risk of Type II error and lower power
• No change in risk of Type II error or power

10. The greater the difference between the Ho claim and the true value of the population parameter,

• The smaller the risk of a Type II error and the smaller the power
• The smaller the risk of a Type II error and the greater the power
• The greater the risk of a Type II error and the smaller the power
• The greater the probability of no charge in Type II error or in power