Quiz: One-Sample z-test

1. A test is conducted for H0: μ = 34, with σ = 5. A sample of size 100 is selected. The standard error of the sampling distribution is
a. 0.05
b. 0.5
c. 5
2. A test is conducted for H0: μ = 20, with σ = 4. A sample of size 36 has equation. The test statistic is
a. 0.35
b. 2.1
c. 12.6
3. A test is conducted for H0: μ = 50 vs. Ha: μ > 50. The test statistic is 2.46. The p-value is
a. 0.0069
b. 0.0138
c. 0.9931
4. A test is conducted for H0: μ = 9.0 vs. Ha: μ < 9.0. The test statistic is –1.44. Correct conclusions are
a. reject H0 at both α = 0.05 and α = 0.10
b. reject H0 at α = 0.05 but do not reject at α = 0.10
c. reject H0 at α = 0.10 but do not reject at α = 0.05

The label on bottles of water reads 12.0 oz. A consumer group claims that the bottles are under-filled. A sample of size 64 has equation. Assume σ = 0.2. Use this data for questions 5 through 11.

5. The null hypothesis is
a. H0 : μ < 12
b. H0 : μ = 12
c. H0 : μ > 12
6. The alternate hypothesis is
a. Ha : μ < 12
b. Ha : μ ≠12
c. Ha : μ > 12
7. The standard error of the sampling distribution is
a. 0.0031
b. 0.025
c. 0.2
8. The value of the test statistic is
a. –2.0
b. –0.5
c. 2.0
9. The p-value is
a. 0.0228
b. 0.0456
c. 0.9972
10. The conclusion is
a. reject H0 at both α = 0.05 and α = 0.10.
b. reject H0 at α = 0.05 but do not reject at α = 0.10.
c. reject H0 at α = 0.10 but do not reject at α = 0.05.
11. If a 99% confidence interval is constructed to estimate μ with a known σ, the correct critical values for z are
a. ±1.96
b. ±2.33
c. ±2.58
12. A sample of size 40 with a sample mean of 8.4 was selected from a population with σ = 1.2. The 95% confidence interval for μ is
a. equation
b. equation
c. equation
13. A 95% confidence interval for μ of (10.8, 16.4) can be interpreted as
a. 95% of all sample means are between 10.8 and 16.4
b. there is 95% confidence that the sample mean is between 10.8 and 16.4
c. there is 95% confidence that the population mean is between 10.8 and 16.4

A sample of 30 women have a mean height of 63.8 inches and assume σ = 2.5 inches. Use this data for questions 15 through 17.

14. The standard error of the sampling distribution is
a. equation
b. equation
c. 2.5
15. The critical value for a 90% confidence interval is
a. 1.28
b. 1.65
c. 1.96
16. The 90% confidence interval is
a. (62.91, 64.89)
b. (63.05, 64.55)
c. (63.21, 64.38)
17. A sample is selected from a population with μ = 18.6 and the 90% confidence interval is (16.8, 18.2). This means
a. an error was made in computation.
b. the wrong confidence level was used.
c. random sampling resulted in a usually low sample mean.
18. Researchers want to predict the mean length of fish within 0.5 inches at the 95% level. If σ = 1.6, how many fish are needed?
a. 30
b. 35
c. 40

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