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L Camping: Cost of a Sleeping Bag How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this tempera-ture range was taken from Backpacker Magazine: Gear Guide (Vol. 25, Issue 157, No. 2). Brand names include American Camper, Cabela's, Camp 7, Caribou, Cascade, and Coleman.

80 90 100 120 75 37 30 23 100 110.:

105 95 105 60 110 120 95 90 60 70

(a) Use a calculator with mean and sample standard deviation keys to verify

that $83.75 and s $28.97. (b) Using the given data as representative of the population of prices of all sum-i

mer sleeping bags, find a 90% confidence interval for the mean price p of alL% summer sleeping bags.

O T1'atol: Avalanches Snow avalanches can be a real problem for travelers in the we

4. stern United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a profes-sor of civil engineering at the University of British Columbia. Slab avalanches studied in Canada had an average thickness of p = 67 cm (Source: Avalanche Handbook, by D. McClung and P. Schaerer). The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm):

59 51 76 38 65 54 49 62

68 55 64 67 63 74 65 79

i. Use a calculator with mean and standard deviation keys to verify that 61.8 cm ands" 10.6 cm.

ii. Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in Canada.

03 0. Wildlife: Coyotes A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be 2.05 years, with sample standard deviation s = 0.82 years (based on information from the book Coyotes: Biology, Behavior and Management by M. Bekoff, Academic Press). However, it is thought that the overall population mean age of coyotes is g = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use a = 0.01.

P. 2-

04 ,. Medical: Red Blood Cell Count Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the popu-lation of healthy female adults, the mean of the x distribution is about 4.8 (based on information from Diagnostic Tests with Nursing Implications, Springhouse Corporation). Suppose that a female patient has taken six labora-tory blood tests over the past several months and that the RBC count data sent to the patient's doctor are

4.9 4.2 4.5 4.1 4.4 4.3

i. Use a calculator with sample mean and sample standard deviation keys to verify that i = 4.40 and s 0.28.

ii. Do the given data indicate that the population mean RBC count for this patient is lower than 4.8? Use a = 0.05.

4p Medical: Hemoglobin Count Let x be a random variable that represents hemo-globin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women (see reference in Problem 15). Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are

15 18 16 19 14 12 14 17 15 11

i. Use a calculator with sample mean and sample standard deviation keys to verify that X = 15.1 and s 2.51.

ii. Does this information indicate that the population average HC for this - patient is higher than 14? Use a = 0.01.

* Fishing: Shore or Boat? Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let row B represent hours per fish caught fishing from the shore, and let row A represent hours per fish caught using a boat. The following data are paired by month from October through April. (Source: Pyramid Lake Fisheries, Paiute Reservation, Nevada.)

.OcL .t(ov.. Dc. Jan F6. March April

B: Shore' 1.6 1.8 2.0 3.2 3.9 3.6 3.3

A: Boat 1.5 1.4 1.6 2.2 3.3 3.0 3.8

Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore.

a. Ecology: Rocky Mountain National Park The following is based on informa-tion taken from Winter Wind Studies in Rocky Mountain National Park, by D. E. Glidden (Rocky Mountain Nature Association). At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Weather Station 1 2 3 4 5

January 139 122 126 64 78

• April 104 113 100 88 61

Does this information indicate that the peak wind gusts are higher in January than in April? Use a = 0.01.

Economics: Cost of Living Index In the following data pairs, A represents the cost of living index for utilities and B represents the cost of living index for transportation. The data are paired by metropolitan areas in the United States. A random sample of 46 metropolitan areas gave the following information. (Reference: Statistical Abstract of the United States, 121st edition.)

A: 90 84 85 106 83 101 89 125 105

B: 100 91 103 103 109 109 94 114 113

A: 118 133 104 84 80 77 90 92 90

B: 120 130 117 109 107 104 104 113 101

A: 106 95 110 112 105 93 119 99 109

S. 96 109 103 107 103 102 101 86 94

A: 109 113 90 121 120 85 91 91 97

B: 88 100 104 119 116 104 121 108 86

A: 95 115 99 86 88 106 80 108 90 87

B: 100 83 88 103 94 125 115 100 96 127

i. _Let d be the random variable d = A — B. Use a calculator to verify that d — —5.739 and sd = 15.910.

ii. Do the data indicate that the U.S. population mean cost of living index for utilities is less than that for transportation in these a reas? Use a = 0.05.

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Q ft. (a) Use a calculator. (b) $72.55 to $94.95. -

i. Use a calculator. Rounded values are used in part ii.

ii. (a) a = 0.01;H0 : = 67; H I : ,u. ­-E67.

(b) Student's t, di = 15; t= -1.962.

(c) 0.050 < P-value < 0.100; on graph, shade area to the right

of 1.962 and to the left of -1.962. From 11-84, P-value = 0.0686.

(d) P-value interval > 0.01; fail to reject H0 .

(e) At the 1 0/6 level of significance, the sample evidence does not support a claim that the average thickness of slab avalanches in Vail is different from that in Canada.

0 i. Use acakulato Rounded values are used in part ii.

ii. (a) a = 0.05; H0 : p. = 4.8; H:p. <4.8.

(b) Student's t, d.f. = 5; -3499.

(C) 0.005 < P-value < 0.010; on graph, shade the area to the

left of -3.499. From 11-84, P- value 0.0086.

(d) P-value interval :5 0.05 for a; reject H0 .

(e) At the 5% level of significance, sample evidence supports the claim that the average RBC count for this patient is less than 4.8.

C(,tc.rkv 17

Use a calculator. Rounded values are used in part ii.

ii. (a) a = 0.01; H0 : p. = 14; H1:i.L> 14.

(b) Student's t, d.f = 9 t 1.386. (c)O.OIL5 < P-value < 0.100; on

a A rt graph, shade area to the right v of 1.386. From 11-84, P-value

0.0996. (d) P-value interval > 0.01; fail to

reject H0 .

(e) At the 1% level of significance, the sample data do not support the claim that the average NC for lhjsoatient is higher than 14.

Q (a)a=fLOlj0 : Ld =0; H1: /2d (b) Student's t, di = 6; d 0.371;

t=2.08. (c) 0.050 < P-value < 0.100; on

graph, shade area to the left of -2.08 and to the right of 2.08. From 11-84, P-value 0.0823.

(d) P-value interval > 0.01 for a; fail to reject H0 .

(e) At the I O/o level of significance, the evidence is insufficient to claim that there is a difference in population mean hours per fish caught between boat fishing and shore shing..__________

V (b) Student's f, d.f = 4; d 12.6; t1.243. 015

(c) P-value <; on

o 1graph, shade area to the right of 1.243. From 11-84, P-value = 0.1408.

(d) P-value interval > 0.01 for a; fail to reject /1g.

(e) At the 1% level of significance, the evidence is insufficient to claim that average peak wind gusts are higher in January.

I. Use a calculator. Non-rounded results are used in part ii.

ii. (a) a = 0.05; H: bLd = 0;

(b) Student's t,di Iç U df

d -5.739; t -2.447.

(c) 0.005 <P-value < 0.010; on graph, shade area to the left of -2.447. From 11-84, P-value 0.0092.

(d) P-value interval 0.05 for a; reject H0 .

(e) At the 5% level of significance, the evidence is sufficient to claim that the population mean cost of living index for utilities is less than that for transportation in these areas.

z (a) a = 0.01; H0 : g = 1.75 yr; Vic H: 4 >1.75 yr.'

(b) Student's t, d.f = 45; t '= 2.481.

(c) 0.005 < P-value < 0.010; on graph, shade area to the right of

2.481. From 11-84, P-value 0.0084.

(d) Entire P-interval :5 0.01 for a; reject H0

(e) At the 1 OA level of significance, the sample data indicate that the average age of the Minnesota region coyotes is higher than 1.75 years.