Question Recent studies have shown that Punica granatum (or pomegranate) seeds have germination time that is found to be normally distributed. To verify this, a biologist measured the number of days to germination of 20 random pomegranate seeds. Below shows the data obtained: 15.82 16.69 17.69 18.14 19.38 16.07 16.89 17.98 18.33 19.48 16.49 17.30 18.10 18.50 19.55 16.67 17.67 18.11 19.35 20.66 Using visual inspection with the given histogram and Q-Q Plot below, do the data show evidence that the germination time of pomegranate seeds follows the normal distribution? Explain by interpreting each graph. Figure 1. Histogram Figure 2. Q-Q Plot 2. Using the Wilk-Shapiro Test with R software output given below, do the data show evidence that the germination time of pomegranate seeds follows the normal distribution at ?=1%? Complete the following steps: Shapiro-Wilk normality test data: time W = 0.9693 , p-value = 0.7401 Ho: Ha: Decision Rule: p-value: Decision: Conclusion: 3. Find a point estimate of the true mean germination time of pomegranate seeds. 4. Given the R software output below, interpret the 90% confidence interval about the true mean germination time of pomegranate seeds. 90 percent confidence interval: 17.44249 18.44451 5. Given the R software output below, is there sufficient evidence to say that the mean germination time of pomegranate seeds is not equal to 18 days, at 5% level of significance? Explain briefly. 95 percent confidence interval: 17.33705 18.54995 6. What happened to the confidence interval after increasing the confidence level? Give the width of the 90% and 95% confidence intervals. 7. At 5% level of significance, test from the data if the mean germination time of pomegranate seeds is not equal to 18 days using the given R-software output: One Sample t- test Data: time t = -0.195 , df = 19, p-value = 0.8475 alternative hypothesis: true mean is not equal to 18 Note: write Ho and Ha both in symbols and in words. Ho: Ha: Test procedure: Decision Rule: Computed test statistic and p-value: Decision: Conclusion: 8. Relate the computed confidence interval (item #5) with the conclusion using the result of the test statistic (p-value) (item #7). Do they give similar conclusion?
Recent studies have shown that Punica granatum (or pomegranate) seeds have germination time that is found to be
|
15.82 |
16.69 |
17.69 |
18.14 |
19.38 |
|
16.07 |
16.89 |
17.98 |
18.33 |
19.48 |
|
16.49 |
17.30 |
18.10 |
18.50 |
19.55 |
|
16.67 |
17.67 |
18.11 |
19.35 |
20.66 |
- Using visual inspection with the given histogram and Q-Q Plot below, do the data show evidence that the germination time of pomegranate seeds follows the normal distribution? Explain by interpreting each graph.
Figure 1. Histogram Figure 2. Q-Q Plot
2. Using the Wilk-Shapiro Test with R software output given below, do the data show evidence that the germination time of pomegranate seeds follows the normal distribution at ?=1%? Complete the following steps:
|
Shapiro-Wilk normality test data: time W = 0.9693 , p-value = 0.7401 |
Ho:
Ha:
Decision Rule:
p-value:
Decision:
Conclusion:
3. Find a point estimate of the true mean germination time of pomegranate seeds.
4. Given the R software output below, interpret the 90% confidence interval about the true mean germination time of pomegranate seeds.
|
90 percent confidence interval: 17.44249 18.44451 |
5. Given the R software output below, is there sufficient evidence to say that the mean germination time of pomegranate seeds is not equal to 18 days, at 5% level of significance? Explain briefly.
|
95 percent confidence interval: 17.33705 18.54995 |
6. What happened to the confidence interval after increasing the confidence level? Give the width of the 90% and 95% confidence intervals.
7. At 5% level of significance, test from the data if the mean germination time of pomegranate seeds is not equal to 18 days using the given R-software output:
|
One Sample t- test Data: time t = -0.195 , df = 19, p-value = 0.8475 alternative hypothesis: true mean is not equal to 18 |
Note: write Ho and Ha both in symbols and in words.
Ho:
Ha:
Test procedure:
Decision Rule:
Computed test statistic and p-value:
Decision:
Conclusion:
8. Relate the computed confidence interval (item #5) with the conclusion using the result of the test statistic (p-value) (item #7). Do they give similar conclusion?
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