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BUGEN1502 Confidence Interval and Hypothesis testing
Assignment 2: Confidence Interval and Hypothesis testing (10 marks)
Background
A researcher is interested in the average time for a package to arrive in Australia from a seller based in Hong Kong. The time is the days from the time of ordering to the time of arrival in Australia (in days). A random sample of the packages is selected. The data is saved in the Excel file BUGEN1502 Assignment 2 data.xls.
Questions
Question 1 (2 Marks)
- Use Excel to obtain an appropriate histogram of the values of the arrival time. The interval in the table is to be used for creating the histogram.
| range | Frequency |
| 0 to 3 | |
| over 3 to 6 | |
| over 6 to 9 | |
| over 9 to12 | |
| over 12 to 15 | |
| over 15 to 18 | |
| over 18 to 21 | |
| over 21 to 24 | |
| over 24 to 27 | |
| over 27 to 30 | |
| over 30 |
Insert the histogram below
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- Briefly state what the histogram is telling us about the distribution of the data.
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- Calculate the descriptive statistics.
Insert the descriptive statistics below
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- Explain the distribution, central tendency and variation.
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Question 2 (2 Marks)
- Calculate the 95% confidence interval of the population mean, assume that the population standard deviation is known (σ = 5.80).
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- Calculate the 95% confidence interval of the population mean, assuming that the population standard deviation is unknown.
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Question 3 (4 marks)
In the past it has been found that the arrival time have a population mean value of μ = 13 days. Assume that the population standard deviation is unknown. The significance level alpha is set at 5%.
- The research wants to know whether this mean has changed. Test the hypothesis with the critical value approach.
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- The research wants to know whether the mean is more than 13 days. Test the hypothesis with p value approach.
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Question 4 (2 Marks)
- Explain the meaning of p value.
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- What is the advantage of p value approach over critical value approach?
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- Does a small p value indicate a strong relationship between the studied variables? Give your reason.
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- If a p value of a one tailed test is 0.04, what is the p value for a two tailed test?
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Expert's Answer
Answer 4
- Explain the meaning of p value.
The P value is the likelihood of obtaining the test results under the assumption when the null hypothesis is right in null hypothesis significance testing.
- What is the advantage of p value approach over critical value approach?
The one value of p-value is enough to tell whether that value is greater or lesser than significance level in order to accept or reject null hypothesis. If that value is less than significance level so we reject null hypothesis.
- Does a small p value indicate a strong relationship between the studied variables? Give your reason.
If p value is smaller so it gives you indicate to reject null hypothesis. Th e p value is statistically significant when it is less than 0.05. As it tells us that there is less than 5% chance whether null hypothesis is correct.
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