(a)
(i)
The level of significance, null and alternative hypothesis.
(a)
(i)
Answer to Problem 10CRP
Solution:
The level of significance is α = 0.05. The null hypothesis is
Explanation of Solution
The level of significance is defined as the probability of rejecting the null hypothesis when it is true, it is denoted by
Null hypothesis
Alternative hypothesis
(ii)
To find:
The sampling distribution that should be used and compute the value of the sample test statistic.
(ii)
Answer to Problem 10CRP
Solution:
The
Explanation of Solution
Calculation:
We will use the normal distribution to binomial, if the condition np > 5 and nq > 5 are satisfied.
Both conditions are met, so we can use normal distribution.
Using
The sample test statistic z is
(iii)
To find:
The P-value of the test statistic and sketch the sampling distribution showing the area corresponding to the P-value.
(iii)
Answer to Problem 10CRP
Solution:
The P-value of the test statistic is 0.1970.
Explanation of Solution
Calculation:
We have z = 1.29
For a two tailed test, the P-value is 0.1970.
Graph:
To draw the required graphs using the Minitab, follow the below instructions:
Step 1: Go to the Minitab software.
Step 2: Go to Graph > Probability distribution plot > View probability.
Step 3: Select ‘Normal’ and Mean = 0, Standard deviation = 1.
Step 4: Click on the Shaded area > X value.
Step 5: Enter X-value as 1.29 and select ‘Both Tail’.
Step 6: Click on OK.
The obtained distribution graph is:
(iv)
Whether we reject or fail to reject the null hypothesisand whether the data is statistically significant for a level of significance of 0.05.
(iv)
Answer to Problem 10CRP
Solution:
The P-value > α, hence we fail to reject the
Explanation of Solution
The P-value of 0.1970 is greater than the level of significance (α) of 0.05. Therefore we don't have enough evidence to reject the null hypothesis
(v)
The interpretation for the conclusion.
(v)
Answer to Problem 10CRP
Solution:
There is not enough evidence to conclude that the students at this school are significantly different from the overall proportion of 16-19 year older who is victims of crime.
Explanation of Solution
The P-value of 0.1970 is greater than the level of significance (
(b)
To find:
The 90% confidence interval for the proportion of students in the school who have been victims of a crime.
(b)
Answer to Problem 10CRP
Solution:
The 90% confidence interval for p is (0.079, 0.221).
Explanation of Solution
Calculation:
We have to find 90% confidence interval. Using,
90% confidence interval is
The 90% confidence interval for p is (0.079, 0.221).
(c)
To find: The minimum
(c)
Answer to Problem 10CRP
Solution:
The sample size is 193 so that the margin of error is not more than 0.05
Explanation of Solution
Calculation:
We have the sample size formula as follows
Therefore n = 193 is the minimum sample size to ensure that the margin of error E is not more than 0.05.
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Chapter 9 Solutions
Understanding Basic Statistics
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