
In Problems 8-12, please use the following steps (i)-(v) for all hypothesis tests:
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
(v) Interpret your conclusion in the context of the application.
Note: For degrees of freedom d.f. not in the Student’s t table, use the closet d.f. that is smaller. In some situation, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative” answer.
Testing and Estimating µ with σ Known Let x be a random variable that represents micrograms of lead per liter of water (µg/L). An industrial plant discharges water into a creek. The Environmental Protection Agency has studied the discharged water and found x to have a
(a) The industrial plant says that the population
(b) Find a 95% confidence interval for µ using the sample data and the EPA value for σ.
(e) How large a sample should be taken to be 95% confident that the sample mean
(a)
(i)

The level of significance, null and alternative hypothesis.
Answer to Problem 8CRP
Solution: The level of significance 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.
Answer to Problem 8CRP
Solution: The normal distributionshould be used. The sample test statisticis 2.53.
Explanation of Solution
Calculation:
We will use the normal distribution because the original distribution x is normal and also
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.
Answer to Problem 8CRP
Solution: The P-value of the test statistic is 0.0057.
Explanation of Solution
Calculation:
We have z = 2.53
Graph:
To draw the required graphs using the Minitab, follow the below instructions:
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 2.53 and select ‘Right 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 0.01.
Answer to Problem 8CRP
Solution: The P-value < α, hence we will reject the
Explanation of Solution
The P-value of 0.0057 is less than the level of significance (α) of 0.01. Therefore we have to reject the null hypothesis
(v)

The interpretation for the conclusion.
Answer to Problem 8CRP
Solution: There is enough evidence to conclude that lead concentration population average is higher than the industrial plant claims.
Explanation of Solution
The P-value of 0.0057 is less than the level of significance (
(b)

To find: A 95% confidence interval for the mean using the sample data.
Answer to Problem 8CRP
Solution:
The 95% confidence interval for
Explanation of Solution
Calculation:
We have to find 95% confidence interval
95% confidence interval is
The 95% confidence interval for
(c)

To find: The minimum sample size so that the margin of error is not more than 0.2
Answer to Problem 8CRP
Solution:
The sample size is 48 so that the margin of error is not more than 0.2
Explanation of Solution
Calculation:
We have the sample size formula as follows
Therefore n = 48 is the minimum sample size to ensure that the margin of error E is not more than 0.2
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Chapter 9 Solutions
UNDERSTANDING BASIC STATISTICS (LOOSE)
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- At the beginning of year 1, you have $10,000. Investments A and B are available; their cash flows per dollars invested are shown in the table below. Assume that any money not invested in A or B earns interest at an annual rate of 2%. a. What is the maximized amount of cash on hand at the beginning of year 4.$ ___________ A B Time 0 -$1.00 $0.00 Time 1 $0.20 -$1.00 Time 2 $1.50 $0.00 Time 3 $0.00 $1.90arrow_forwardFor each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). Year Month Rate (%)2009 Mar 8.72009 Apr 9.02009 May 9.42009 Jun 9.52009 Jul 9.52009 Aug 9.62009 Sep 9.82009 Oct 10.02009 Nov 9.92009 Dec 9.92010 Jan 9.82010 Feb 9.82010 Mar 9.92010 Apr 9.92010 May 9.62010 Jun 9.42010 Jul 9.52010 Aug 9.52010 Sep 9.52010 Oct 9.52010 Nov 9.82010 Dec 9.32011 Jan 9.12011 Feb 9.02011 Mar 8.92011 Apr 9.02011 May 9.02011 Jun 9.12011 Jul 9.02011 Aug 9.02011 Sep 9.02011 Oct 8.92011 Nov 8.62011 Dec 8.52012 Jan 8.32012 Feb 8.32012 Mar 8.22012 Apr 8.12012 May 8.22012 Jun 8.22012 Jul 8.22012 Aug 8.12012 Sep 7.82012 Oct…arrow_forwardFor each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). Date IBM9/7/2010 $125.959/8/2010 $126.089/9/2010 $126.369/10/2010 $127.999/13/2010 $129.619/14/2010 $128.859/15/2010 $129.439/16/2010 $129.679/17/2010 $130.199/20/2010 $131.79 a. Construct a line chart of the closing stock prices data. Choose the correct chart below.arrow_forward
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