Chapter 9 and 10 Problems Overview Template

H0 ≤ 52 H1 > 52 Label Sample Hypothesized Mean (μ) Mean SD n One-tailed alpha two-tailed alpha One-tailed test test statistic (Z score) Status Use NORM.S.DIST to convert Z score to probability 1 minus the probability gives the p value One-tailed alpha A phone industry manager thinks that customer monthly cell phone bill have increased, and now ave claim. Assume population SD = 10 is known. Test at the 90% confidence level. critical value z a H 0 : μ ≤ 52 the average is not over $52 per month H 1 : μ > 52 the average is greater than $52 per month (i.e., sufficient evidence exists to support the Suppose a sample is taken with the following results: n = 64, x = 53.1 (  = 10 was assumed known

erage over $52 per month. The company wishes to test this e manager’s claim) n) α 0 0 z n σ μ x z if H Reject    ) μ μ | n σ/ μ - x P(z true) is H that given , n σ/ μ - x P(z value - p 0 0 0 0     

H0 = 3 H1 ≠ 3 Label Sample Hypothesized Mean (μ) Mean SD n One-tailed alpha two-tailed alpha two-tailed test test statistic (Z score) Status Use NORM.S.DIST, and then multiply p by 2 two-tailed alpha x 2 critical value z a Test the claim that the true mean # of TV sets in US homes is equal to 3. Sample size of 100 with sample mean of 2.84 (Assume σ = 0.8). Test at 90% confidence level.

Store # Broccoli Broccoli Price Peas Peas Price 1 890 $1.08 9557 0.79 2 17,630 $0.69 19452 0.68 3 6,831 $0.59 520 0.79 4 1,248 $0.70 460 0.79 5 413 $0.78 586 0.79 6 21,145 $0.69 2493 0.9 7 8,643 $0.94 3085 0.93 8 2,178 $1.03 18867 0.75 9 590 $0.70 369 0.79 10 3,154 $1.00 22639 0.68 11 830 $0.71 494 0.79 12 413 $0.77 624 0.79 13 2,614 $0.77 23438 0.62 14 430 $0.78 616 0.79 15 2,184 $0.89 32985 0.59 16 2,910 $0.59 404 0.79 17 1,762 $0.85 2651 0.89 18 710 $0.67 857 0.65 19 272 $0.83 420 0.79 20 6,439 $0.66 6295 0.82 21 4,521 $0.80 13258 0.75 22 14,129 $0.69 3806 0.92 23 1,641 $0.96 8525 0.83 24 1,063 $0.67 725 0.79 25 27,254 $0.69 4367 0.93 26 1,534 $0.88 6919 0.74 27 2,062 $0.88 3881 0.8 28 6,954 $1.07 2386 1.06 29 2,006 $0.91 17091 0.76 30 11,996 $0.71 3398 0.9 31 11,761 $0.65 4049 0.78 32 440 $0.78 640 0.79 33 2,647 $0.92 4149 0.91 34 12,485 $0.70 13473 0.65 35 2,793 $0.84 4485 0.86 36 2,262 $0.85 3814 0.89 37 1,258 $1.08 14916 0.85 38 1,789 $1.08 2030 1.07 39 667 $0.81 572 0.79 40 3,290 $1.00 4163 0.98 Grand Junction Vegetables is a producer of a wide variety of frozen vegetables. The c of frozen broccoli has increased. The mean weekly number of sales per store has bee data from 134 stores for your study (see below). Assume a confidence level of 95%.

41 1,316 $0.98 21245 0.69 42 2,598 $0.63 15607 0.65 43 470 $0.83 713 0.79 44 3,367 $0.94 3741 0.85 45 2,837 $0.84 4639 0.86 46 156 $0.83 257 0.79 47 1,363 $0.97 2122 0.92 48 22,867 $0.69 1967 1.02 49 1,203 $0.59 2235 1.05 50 9,431 $0.73 31501 0.69 51 424 $0.79 596 0.79 52 1,564 $0.92 24212 0.69 53 4,539 $0.81 5032 0.91 54 341 $0.84 636 0.79 55 2,677 $1.06 3008 1.05 56 2,435 $1.02 13505 0.79 57 1,634 $0.93 2831 1.06 58 5,847 $0.78 3778 0.92 59 3,280 $0.83 17133 0.78 60 2,461 $0.87 7529 0.82 61 2,966 $0.57 382 0.76 62 6,560 $0.75 3407 0.9 63 816 $0.71 573 0.79 64 2,534 $1.03 3783 1.02 65 472 $0.78 745 0.79 66 2,257 $0.85 14627 0.43 67 476 $0.82 778 0.79 68 2,556 $0.90 9125 0.77 69 2,281 $0.99 2330 0.93 70 673 $0.66 957 0.65 71 637 $0.67 748 0.65 72 1,684 $0.95 1951 1.07 73 3,415 $0.62 7321 0.77 74 2,670 $0.57 508 0.76 75 3,773 $0.69 17644 0.63 76 20,383 $0.63 9755 0.65 77 4,658 $0.46 10753 0.67 78 2,110 $0.82 16457 0.77 79 448 $0.81 779 0.79 80 607 $0.67 811 0.65 81 1,426 $0.93 11785 0.76 82 401 $0.83 604 0.79 83 2,719 $1.03 2947 1.02 84 367 $0.82 568 0.79 85 2,371 $1.03 3143 1.01 86 440 $0.83 700 0.79 87 467 $0.68 645 0.65

Label Sample d Mean (μ) Mean SD n DF One-tailed alpha two-tailed alpha One-tailed test test statistic (t score) Status Use T.DIST to convert T score to probability 1 minus the probability gives the p value One-tailed alpha company president has asked you to determine if the weekly sales of 16 ounce packages en 2,400 packages over the past 6 months. You have obtained a random sample of sales critical value t a H 0 : μ ≤ 2,400 H 1 : μ > 2,400

Label Sample d Mean (μ) Mean SD n DF One-tailed alpha two-tailed alpha two-tailed test test statistic (t score) Status Use T.DIST to convert T score to probability 1 minus the probability gives the p value, then multiply by 2 two-tailed alpha x 2 critival value t a The average cost of a hotel room in Chicago is said to be $168 per night. A random sample of 25 hotels r x = $172.50 s = $15.40. Test at the  = 0.05 level. (Assume the population distribution is normal) H 0 : μ = 168 H 1 : μ ¹ 168

Sample Null Proportion Failure n One-tailed alpha two-tailed alpha test statistic (Z score) Use NORM.S.DIST, and then multiply p by 2 two-tailed alpha x 2 A marketing company claims that it receives 8% responses from its mailing. To test this claim, a random with 25 responses. Test at the ALPHA = .05 significance level. critical value z a H 0 : P = 0.08 H 1 : P ¹ 0.08

m sample of 500 were surveyed

he length of the bolts follows a normal an length of their bolts is 60 mm, and so probability of a type II error if the actual n σ/ z μ α 0  

This is the Power of the Test

d items. items against the alternative .