|
Determine the critical values for the following tests of the population mean with an unknown population standard deviation. The analysis is based on 19 observations drawn from a normally distributed population at a 5% level of significance. Use Table 2. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.) |
| Critical Value | ||
|
a. |
H0: μ ≤ 52 versus HA: μ > 52 |
|
| b. | H0: μ = 12.0 versus HA: μ ≠ 12.0 | ± |
| c. | H0: μ ≥ 2.0 versus HA: μ < 2.0 | |
| d. | H0: μ = 16 versus HA: μ ≠ 16 | ± |
Solution :
Degrees of freedom = 19 - 1 = 18
Using t
| Critical Value | ||
|
a. |
H0: μ ≤ 52 versus HA: μ > 52 |
1.734 |
| b. | H0: μ = 12.0 versus HA: μ ≠ 12.0 | ± 2.101 |
| c. | H0: μ ≥ 2.0 versus HA: μ < 2.0 | -1.734 |
| d. | H0: μ = 16 versus HA: μ ≠ 16 | ± 2.101 |
Determine the critical values for the following tests of the population mean with an unknown population standard dev...
Consider the following hypotheses: H0: μ = 4,900 HA: μ ≠ 4,900 The population is normally distributed with a population standard deviation of 600. Compute the value of the test statistic and the resulting p-value for each of the following sample results. For each sample, determine if you can "reject/do not reject" the null hypothesis at the 10% significance level. (You may find it useful to reference the appropriate table: z table or t table) (Negative values should be indicated...
For a given population, suppose we wish to test H0:μ=20 versus H0:μ=20 at α=0.1 . If we plan to take a random sample of 16 observations from a normally distributed population with unknown variance, then what is the critical value (or rejection point) for this test?
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the 0.025 significance level. H0: μ ≥ 220 H1: μ < 220 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is the value of the...
A sample of 44 observations is selected from one population with a population standard deviation of 3.1. The sample mean is 101.0. A sample of 56 observations is selected from a second population with a population standard deviation of 5.0. The sample mean is 99.5. Conduct the following test of hypothesis using the 0.10 significance level. H0 : μ1 = μ2 H1 : μ1 ≠ μ2 Is this a one-tailed or a two-tailed test? One-tailed test Two-tailed test State the...
Consider the following hypotheses: H0: μ = 420 HA: μ ≠ 420 The population is normally distributed with a population standard deviation of 72. Use Table 1. a. Use a 1% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.) Critical value(s) ± b-1. Calculate the value of the test statistic with x−x− = 430 and n = 90. (Round your intermediate calculations to 4 decimal places and final answer to...
Consider the following hypotheses: H0: μ = 9,100 HA: μ ≠ 9,100 The population is normally distributed with a population standard deviation of 700. Compute the value of the test statistic and the resulting p-value for each of the following sample results. For each sample, determine if you can "reject/do not reject" the null hypothesis at the 10% significance level. (You may find it useful to reference the appropriate table: z table or t table) (Negative values should be indicated...
Consider the following hypotheses: H0: μ ≥ 160 HA: μ < 160 The population is normally distributed. A sample produces the following observations: 152 138 151 144 151 142 Conduct the test at the 1% level of significance. (You may find it useful to reference the appropriate table: z table or t table) a. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and...
Determine the critical region and the critical values used to test the following null hypotheses. (Assume a Z-test statistic is appropriate here.) (a) H0: μ = 60 (≥), Ha: μ < 60, α = 0.01 ---Select--- less than or equal to greater than or equal to at least as extreme as at most as extreme as ---sign--- + - ± (b) H0: μ = −83 (≥), Ha: μ < −83, α = 0.1 ---Select--- less than or equal to greater than...
A sample of 44 observations is selected from one population with a population standard deviation of 3.9. The sample mean is 102.0. A sample of 46 observations is selected from a second population with a population standard deviation of 5.6. The sample mean is 100.3. Conduct the following test of hypothesis using the 0.10 significance level. H0 : μ1 = μ2 H1 : μ1 ≠ μ2 Is this a one-tailed or a two-tailed test? One-tailed test Two-tailed test State the...
Consider the following hypothesis test:H0 : μ = 16Ha : μ ≠ 16A sample of 50 provided a sample mean of 14.34. The population standard deviation is 7. a. Compute the value of the test statistic (to 2 decimals).b. What is the p-value (to 4 decimals)? c. Using α = .05, can it be concluded that the population mean is not equal to 1?d. Using α = .05, what are the critical values for the test statistic (to 2 decimals)?e. State the rejection...