The fill volume of a particular lubricant is normally distributed with a mean of 10 liters. Suppose we randomly select 10 containers and we find that the sample mean is 10.06 liters and the sample standard deviation is 0.25 liters. You are asked to conduct a hypothesis test at the alpha = 0.05 level of significance to determine if the mean fill volume of the lubricant is greater than 10 liters. What null and alternative hypotheses would you use to conduct this test? Ho: mu= 10 and H1: mu> 10 Ho: mu = 10 and H1: mu = 10.06 Ho: x = 10.6 and H1: x > 10.06 Ho: p = 10 and H1: p > 10 What type of test statistic would you use to conduct this test? z test statistic t test statistic If you were to use a confidence interval rather than a hypothesis test to determine if the mean fill volume of the lubricant is greater than 10 liters, what would be your best choice for a confidence interval so that it directly corresponds to the hypothesis test? 95% one sided lower bound 95% two sided Cl 95% one sided upper bound 90% one sided upper bound If your confidence interval covers 10, your decision and conclusion would be which of the following. Decision: Do not reject H0. Conclusion: We have enough evidence at the alpha = 0.05 level of significance to show that that the mean volume is less than 10 liters. Decision: Do not reject H0. Conclusion: We do not have enough evidence at the alpha = 0.05 level of significance to show that the mean volume is greater than 10 liters. Decision: Do not reject H1 Conclusion: We have enough evidence at the alpha = 0.05 level of significance to show that that the mean volume is less than 10 liters. Decision: Reject H0 Conclusion: We have enough evidence at the alpha = 0.05 level of significance to show that the mean volume is greater than 10 liters.
9). Option a
H_0: \\mu =10 \\ \\ H_1: \\mu > 10
10). Option b t test statistic
11). Option c
95% one side upper bound
12).
Option b
Decision : Do not Reject H0. We do not have enough evidence at 0.05 level of significance to that the mean volume is greater than 10 litres.
t Test for Hypothesis of the Mean
Data
Null Hypothesis mean =
10
Level of Significance
0.05
Sample Size
10
Sample Mean
10.06
Sample Standard Deviation
0.25
Intermediate Calculations
Standard Error of the Mean
0.0791
Degrees of Freedom
9
t Test Statistic
0.7589
Upper-Tail Test
Upper Critical Value
1.8331
p-Value
0.2336
Do not reject the null hypothesis
| t Test for Hypothesis of the Mean |
| |
| Data |
| Null Hypothesis mean = | 10 |
| Level of Significance | 0.05 |
| Sample Size | 10 |
| Sample Mean | 10.06 |
| Sample Standard Deviation | 0.25 |
| |
| Intermediate Calculations |
| Standard Error of the Mean | 0.0791 |
| Degrees of Freedom | 9 |
| t Test Statistic | 0.7589 |
| |
| Upper-Tail Test | |
| Upper Critical Value | 1.8331 |
| p-Value | 0.2336 |
| Do not reject the null hypothesis | |
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