A+ Work 18.48 18.49 18.50 18.51 18.52 & 18.54

18.48- Researchers at Miami University in Oxford, Ohio, investigated the use of p charts to monitor the market share of a product and to document the effectiveness of marketing promotions. Market share is defined as the company’s proportion of the total number of products sold in a category. If a p chart based on a company’s market share indicates an in-control process, then the company’s share in the marketplace is deemed to be stable and consistent over time. In the example given in the article, the RudyBird Disk Company collected daily sales data from a nationwide retail audit service. The first 30 days of data in the accompanying table(stored in RudyBird ) indicate the total number of cases of computer disks sold and the number of RudyBird disks sold. The final 7 days of data were taken after RudyBird launched a major in-store promotion. A control chart was used to see if the in-store promotion would result in special cause variation in the marketplace.
Cases Sold Before the Promotion
Day Total RudyBird Day 1 154 35 16 2 153 43 17 3 200 44 18 4 197 56 19
5 194 54 20
6 172 38 21
7
190 43 22 8 209 62 23 9 173 53 24 Total 177 143 200 134 192 155 135 189 184 RudyBird
56
43
69
38
47
45
36
55
44 10
11
12
13
14
15 Day 31 32 33 34 35 36 37 171 173 168 184 211 179 39
44
37
45
58 35 25 26 27 28
29 30 Total 201 177 205 199 187 168 198 170 178 167 204 183 169 47
48
42
71
64
43 RudyBird
92
76
85
90
77
79
197 a. Construct a p chart, using data from the first 30 days (prior to the promotion) to monitor the market share for RudyBird disks.
b. Is the market share for RudyBird in control before the start of the in­store promotion?
c. On your control chart, extend the control limits generated in (b) and plot the proportions for days 31 through 37.
What effect, if any, did the in­store promotion have on RudyBird’s market share? 18.49
18.49 The manufacturer of Boston and Vermont asphalt shingles constructed control charts and analyzed several quality characteristics. One characteristic of interest is the strength of the sealant on the shingle. During each day of production, three shingles are tested for their sealant strength. (Thus, a subgroup is operationally defined as one day of production, and the sample size for each subgroup is 3.) Separate pieces are cut from the upper and lower portions of a shingle and then reassembled to simulate shingles on a roof. A timed heating process is used to simulate the sealing process. The sealed shingle pieces are pulled apart, and the amount of force (in pounds) required to break the sealant bond is measured and recorded. This variable is called the sealant strength. The file Sealant contains sealant strength measurements on 25 days of production for Boston shingles and 19 days for Vermont shingles.
For the 25 days of production for Boston shingles,
a. construct a control chart for the range.
b. construct a control chart for the mean.
c. is the process in control?
d. Repeat (a) through (c), using the 19 production days for Vermont shingles. 18.50 A professional basketball player has embarked on a program to study his ability to shoot foul shots. On each day in which a game is not scheduled, he intends to shoot 100 foul shots. He maintains records over a period of 40 days of practice, with the results stored in Foulspc :
a. Construct a p chart for the proportion of successful foul shots. Do you think that the player’s foul­shooting process is in statistical control? If not, why not?
b. What if you were told that the player used a different method of shooting foul shots for the last 20 days? How might this information change your conclusions in (a)?
c. If you knew the information in (b) prior to doing (a), how might you do the analysis differently?