Statistics Lab Chapter 7 and 8 | Complete Solution

Statistics Lab Chapter 7 and 8

(Confidence Intervals are from Chapter 6 but are incorporated here)
Write the null and alternative in terms of the appropriate parameter (ex. H0: µ=10).  Clearly identify all pieces requested.  Based on what is asked you will need to decide if you are using a one sample or two sample test about the mean large samples or small samples, proportion, or standard deviation.

1.    A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 920 milligrams.  A random sample of 44 breakfast sandwiches has a mean sodium content of 925 with a standard deviation of 18 milligrams.  At α = 0.10, do you have enough evidence to reject the restaurant’s claim?

a.    Null hypothesis:

b.    Alternative hypothesis:

c.    Test statistic:

d.    Critical value(s) and region(s); sketch the distribution:

e.    P-value:

f.    The 90% confidence interval:

g.    Conclusion:  State whether you are accepting or rejecting the null.  ALSO TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.  BEING “WORDY” IS O.K.

h.    Based on whether you failed to reject the null hypothesis or rejected the null hypothesis, what type of error might have been committed, a Type I error or a Type II error?  Explain.

2.    A polling agency claims that over 40% of adults shop for a gift within a week of an event.  In a random survey of 2730 people in the United States, 1130 said they shop for a gift within a week on an event.  Test the agency’s claim at the α = 0.10 level.  What can you conclude?

a.    Null hypothesis:

b.    Alternative hypothesis:

c.    Test statistic:

d.    Critical value(s) and region(s); sketch the distribution:

e.    P-value:

f.    The 90% confidence interval:

g.    Conclusion:  State whether you are accepting or rejecting the null.  ALSO TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.  BEING “WORDY” IS O.K.

h.    In this problem, the normal distribution was used as an approximation to the binomial.  Show that the conditions were met to use the normal distribution.

3.    For this problem, you will use the confidence interval to make a decision and answer the question. In a study of the effects of prenatal cocaine use on infants, the following sample data were obtained for weights at birth:  n = 190,    g, s = 645g (based on data from “Cognitive Outcomes of Preschool Children With Prenatal Cocaine Exposure” by Singer, et al, Journal of the American Medical Association, Vol. 291, No. 20).  It is known that the mean weight for babies born to mothers who do not use cocaine is 3103g. Is there convincing evidence to conclude that birth weights are affected by cocaine use?

a.    Construct a 99% confidence interval:

b.    Does the confidence interval contain the value 3103g, the mean weight for babies born to mothers who do not use cocaine?

Based on the confidence interval, is there convincing evidence to conclude that birth weights are affected by cocaine use?  Explain your answer:
 
4.    Does the growth of trees vary more when the trees are young?  The International Tree Ring Data Base collected data on a particular 440-year-old Douglas fir tree (C.J. Earle, L.B. Brubaker, and G. Segura, International Tree Ring Data Base, NOAA/NGDC Paleoclimatology Program, Boulder, CO).  The standard deviation of the annual ring growth in the tree’s first 80 years of life was 0.8 millimeters per year.  We are interested in testing whether the population standard deviation of annual ring growth in the tree’s later years is less than 0.8mm per year.  The sample variance for a random sample of size 101 taken from the tree’s later years is s2 = 0.3136.  Assume a level of significance of 0.05.

a.    Null hypothesis:

b.    Alternative hypothesis:

c.    Test statistic:

d.    Critical value(s) and region(s); sketch the distribution:

e.    P-value (you will have to use StatCrunch or Minitab to get this):

f.    The 95% confidence interval:

g.    Conclusion:  State whether you are accepting or rejecting the null.  ALSO TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.  BEING “WORDY” IS O.K.

h.    Based on whether you failed to reject the null hypothesis or rejected the null hypothesis, what type of error might have been committed, a Type I error or a Type II error?  Explain.

 
Lab Chapter 8

Perform a hypothesis test for the following problems.  Clearly identify the parameters in the hypotheses. You don’t have to find the confidence intervals, although they are easily obtained using technology.

1.    In 2013, 74 recent graduates of Farmington High School took the Accuplacer at San Juan College and 43 of those graduates placed into developmental math.  For the same year, 74 recent graduates of Piedra Vista High School took the Accuplacer at San Juan College and 58 of those graduates placed into developmental math (San Juan College Office of Institutional Research, July 2014).  At a level of significance of 0.05, test the claim that the proportion of graduates that placed into developmental math was higher for Piedra Vista High School graduates than for Farmington High School graduates.

i.    Null hypothesis:

j.    Alternative hypothesis:

k.    Test statistic:

l.    Critical value(s) and region(s); sketch the distribution:

m.    P-value:

n.    Conclusion:  State whether you are accepting or rejecting the null.  ALSO TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.  BEING “WORDY” IS O.K.

o.    In this problem, the samples need to be large enough to use a normal sampling distribution.  You will need to pool the proportions as shown in section 8-4. Show these conditions are met.

2.    Many studies have been conducted to test the effects of marijuana use on mental abilities.  In one such study, groups of light and heavy users of marijuana in college were tested for memory recall, with the results given below (based on data from “The Residual Cognitive Effects of heavy marijuana Use in College Students” by Pope and Yurgelun-Todd, journal of the American Medical Association, Vol. 275, No. 7).  Use a 0.01 significance level to test the claim that the population of heavy marijuana users has a lower mean than the light users.

Items sorted correctly by light marijuana users: , ,
Items sorted correctly by heavy marijuana users:  , ,

a.    Null hypothesis:

b.    Alternative hypothesis:

c.    Test statistic:

d.    Critical value(s) and region(s); sketch the distribution:

e.    P-value:

f.    Conclusion:  State whether you are accepting or rejecting the null.  ALSO TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.  BEING “WORDY” IS O.K.

g.    Based on whether you failed to reject the null hypothesis or rejected the null hypothesis, what type of error might have been committed, a Type I error or a Type II error?  Explain.

3.    The following table lists SAT scores before and after a sample of 10 students took a preparatory course:

Student       A       B       C       D       E       F       G       H       I       J
SAT score before course (x)    700    840    830    860    840    690    830    1180    930    1070
Sat score after course (y)    720    840    820    900    870    700    800    1200    950    1080

Is there sufficient evidence to conclude that the preparatory course is effective in raising test scores?  Use a 0.05 significance level.

a.    Null hypothesis:

b.    Alternative hypothesis:

c.    Test statistic:

d.    Critical value(s) and region(s); sketch the distribution:

e.    P-value:

f.    Conclusion:  State whether you are accepting or rejecting the null.  ALSO TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.  BEING “WORDY” IS O.K.

g.    Based on whether you failed to reject the null hypothesis or rejected the null hypothesis, what type of error might have been committed, a Type I error or a Type II error?  Explain.
 
4.    An office furniture manufacturer installed a new adhesive application process and claims that the new process has on average pounds of pressure that is greater than the old process.  To compare the new process with the old process, random samples were selected from the two processes and “pull tests” were performed to determine the number of pounds of pressure that were required to pull apart the glued parts.  (This kind of test is an example of destructive testing.)  Let the following be the data collected:

Pounds of pressure needed for the new process:

1250 1210 990 1310 1320 1200 1290 1360 1120 1360 1310 1110 1320 980 950 1430 960 1050 1310 1240 1420 1170 1470 1060

Pounds of pressure needed for the old process:

1180 1360 1310 1190 920 1060 1440 1010 1310 980 1310 1030 960 800 1280 1080 930 1050 1010 1310 940 860 1450 1070

At α = 0.05, is there enough evidence to support the manufacturer’s claim?

Assume the population variances are equal.

a.    Null hypothesis:

b.    Alternative hypothesis:

c.    Test statistic:

d.    Critical value(s) and region(s); sketch the distribution:

e.    P-value:

f.    Conclusion:  State whether you are accepting or rejecting the null.  ALSO TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION.  BEING “WORDY” IS O.K.