Elements of Statistics Unit 3 Problem Set

	Unit 3 Problem Set
	Unit 3 Problem Set						NAME:
	Elements of Statistics--FHSU Virtual College--Fall 2014

	REMEMBER, these are assessed preparatory problems related to the content of Unit 3. The Unit 3 Exam will consist of similar types of problems, but not exactly the same. Thus, make sure you are thinking about the concepts and procedures you studied in this unit versus simply “copying” the process of an example problem. Also, take time to examine the complete objective list in the Unit 3 Review document. All answers should be calculated, as needed, within this Excel sheet, and final concluding answers given directly below or to the right of the problem. Please make your answers are easily found--for example use a different color (not red) of font. No numerical answer resulting from a calculation will be accepted unless the process is performed in Excel and formulas/calculations used are evident when the cell is selected.








	Also, note that the templates for hypothesis testing provided in the Excel Guides for this unit are also given in the next worksheet in this document--see folder tabs at the bottom of the sheet. You may use these templates by copying from the second worksheet, pasting the copy to the right of the associated problem, then changing values as needed. This set of problems is due on 11/25/14.



Problems related to text's Chapter 7 (7-3 to 7-4)
	1.	Determine the two chi-squared (χ²) critical values for the following confidence levels and sample sizes.
		a.	95% and n=36



		b.	99% and n=18





	2.	We are also interested in estimating the population standard deviation (σ) for all FHSU students' IQ score. We will assume that IQ scores are at least approximately normally distributed. Below are the IQ scores of 30 randomly chosen students from FHSU campus.

		135	127	104	139	133	114	110	137	141	118
		115	118	121	141	112	134	115	132	132	118
		127	116	136	132	117	129	116	109	115	129
		Construct a 95% confidence interval estimate of sigma (σ), the population standard deviation.






	3.	Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation. Thus, based upon the information provided for each situation below, determine which (t-, z- or neither) distribution is appropriate. Then if you can use either a t- or z- distribution, give the associated critical value (critical t- or z- score) from that distribution to reach the given confidence level.





		a.	95% confidence	n=40	σ known	population data believed to be normally distributed
			Appropriate distribution:
			Associated critical value:

		b.	90% confidence	n=31	σ unknown	population data believed to be normally distributed
			Appropriate distribution:
			Associated critical value:

		c.	99% confidence	n=29	σ unknown	population data believed to be skewed right
			Appropriate distribution:
			Associated critical value:

		d.	98% confidence	n=100	σ known	population data believed to be very skewed
			Appropriate distribution:
			Associated critical value:


Problems related to text's Chapter 8 (8-1 to 8-4)
	4.	(Multiple Choice) A hypothesis test is used to test a claim. Suppose the test is left-tailed and the critical value is -2.75. If the collected sample's test statistic is -2.15, which of the following is the correct decision statement for the test?

		A.	Fail to reject the null hypothesis
		B.	Fail to reject the alternative hypothesis
		C.	Reject the null hypothesis
		D.	Reject the alternative hypothesis


	5.	(Multiple Choice) A hypothesis test is used to test a claim. Suppose the P value for a hypothesis test is .008, and the significance level is 0.01. Then which of the following is the correct decision statement for the test?

		A.	Fail to reject the null hypothesis
		B.	Fail to reject the alternative hypothesis
		C.	Reject the null hypothesis
		D.	Reject the alternative hypothesis


	6.	(Multiple Choice) Type II error is:
		A.	Rejecting a true null hypothesis
		B.	Rejecting a false null hypothesis
		C.	Failing to reject a false null hypothesis
		D.	Failing to reject a true null hypothesis


	7.	It is claimed that more than 75% of college students in Kansas take education loans. Last year 97 out of 120 randomly selected college students from Kansas reported that they had student loans. Conduct a hypothesis test to determine if the proportion of students who have student loan is more than 75% as claimed. Use a 10% significance level.



		a.	Is the above information sufficient for you to be absolutely certain that more than 75% of all students of Kansas have education loans? Why or why not?




		b.	In establishing a statistical hypothesis testing of this situation, give the required null and alternative hypotheses for such a test, if the claim is that more than 75% of the Kansas college students have education loans.

				H₀:
				H₁:


		c.	Based on your answer in part b, should you use a right-tailed, a left-tailed, or a two-tailed test? Briefly explain how one determines which of the three possibilities is to be used.







		d.	Describe the possible Type I error for this situation--make sure to state the error in terms of the percent of Kansas college students with education loans.





		e.	Describe the possible Type II error for this situation--make sure to state the error in terms of the percent of Kansas college students with education loans.






		f.	Determine the appropriate critical value(s) for this situation.



		g.	Determine/calculate the value of the sample test statistic.



		h.	Detemine the P-value.



		i.	Based upon your work above, is there statistically sufficient evidence in this sample to support that more than 75% of Kansas college students have education loans? Briefly explain your reasoning.







	8.	It is claimed that the national average for the price of gasoline is $3.42 per gallon. Listed below are gas prices from a sample of 32 gas stations from Kansas. At the 5% significance level, follow the steps below to conduct a hypothesis test determine if the average price of gasoline in Kansas is significantly different than the national average of $3.42.


			3.15	3.27	3.14	3.38	3.49	3.12	3.22	3.31
			3.58	3.76	3.26	3.59	3.73	3.12	3.62	3.52
			3.08	3.28	2.98	3.33	3.48	3.18	3.28	3.28
			3.48	3.46	3.48	3.11	3.48	2.88	3.23	3.48


		a.	Give the null and alternative hypotheses for this test in symbolic form.
				H₀:
				H₁:

		b.	Determine the value of the test statistic.



		c.	Determine the appropriate critical value(s).



		d	Detemine the P-value.



		e.	Is there sufficient evidence to support the claim that average price of gasoline in Kansas is significantly different than the national average of $3.42.





Problems related to text's Chapter 9 (9-4)
	9.	Captoril is a drug to lower systolic blood pressure. When seven randomly selected subjects were treated with this drug, their systolic pressure reading (in MM Hg) were measured before and after the drug was taken. Using a 1% significance level, is there sufficient evidence to support the claim that Captoril is effective in lowering the systolic blood pressure? Perform an appropriate hypothesis test showing necessary statistical evidence to support your final given conclusion.




				PreTest	PostTest
				200	160
				175	171
				198	177
				170	167
				193	176
				209	183
				155	145





Problems related to text's Chapter 10 (10-1 to 10-3)
	10.	Multiple Choice:
		For each of the following data sets, choose the most appropriate response from the choices below the table.
			Data Set #1				Data Set #2
			x	y			x	y
			7.4	23.9			-1	-4
			23.9	75.1			-2	-10
			16.6	55.7			2	5
			21.8	68.5			3	4
			7	22			-3	-19
			13.5	48.3			6	-10
			20.9	67.7			7	-20
			9.7	30.5			-1	-4
			10.4	36			0	1
		A.	A strong positive linear relation exists			A.	A strong positive linear relation exists
		B.	A strong negative linear relation exists			B.	A strong negative linear relation exists
		C.	A curvilinear relation exists			C.	A nonlinear relation exists
		D.	No relation exists			D.	No relation exists



	11.	Create a paired data set with five data points (i.e., five x-values and five corresponding y-values) with a strong (but not perfect) positive linear correlation. Determine the correlation coefficient value for your data.

			x	y








	12.	To answer the following, use the list below that contains information on the age of 12 female staffs in FHSU and their corresponding pulse rate.

			Ages	Pulse rates
			42	98
			34	80
			49	98
			27	63
			42	84
			18	49
			41	80
			21	55
			21	56
			19	53
			19	61
			30	74

		a.	Construct a scatterplot for this data set in the region to the right (ages as the independent variable, and pulse rate as the dependent.)


		b.	Based on the scatterplot, does it look like a linear regression model is appropriate for this data? Why or why not?




		c.	Add the line-of-best fit (trend line/linear regression line) to your scatterplot. Give the equation of the trend line below.



		d.	Determine the value of the correlation coefficient. Explain what the value tells you about the data pairs?






		e.	Does the value of the correlation coefficient tell you there is or is not statistically significant evidence that a linear correlation exists between the variables? Explain your position. (HINT: application of table A-6 is needed!)






		f.	What is the predicted pulse rate of a female staff who is 50 years old.




		g.	What is the predicted age of a female staff whose pulse rate is 64?

11 years ago

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Elements of Statistics Unit 3 Problem Set

1. Determine the two chi-squared (χ2) critical values for the following confidence levels and sample sizes.

Determine the two chi-squared (χ2) critical values for the following confidence levels and sample sizes.