PLEASE SHOW EACH AND EVERY STEP. THANK YOU!!! Customer Customer Size Days Amount
ID: 3223355 • Letter: P
Question
PLEASE SHOW EACH AND EVERY STEP. THANK YOU!!!
Customer Customer Size Days Amount 1 Large 12 1352 2 Small 20 274 3 Small 20 267 4 Small 21 229 5 Large 14 1870 6 Small 29 246 7 Large 14 840 8 Medium 19 743 9 Large 18 1245 10 Small 18 195 11 Medium 19 608 12 Large 14 994 13 Small 17 215 14 Small 19 131 15 Medium 17 583 16 Medium 13 501 17 Medium 17 391 18 Medium 25 741 19 Medium 32 708 20 Small 11 235 21 Small 21 236 22 Medium 16 531 23 Medium 20 654 24 Small 30 92 25 Medium 26 447 26 Small 21 198 27 Large 14 1488 28 Small 27 170 29 Medium 25 667 30 Small 14 184 31 Medium 24 277 32 Small 24 204 33 Small 11 198 34 Medium 18 217 35 Small 21 317 36 Large 23 1450 37 Small 16 242 38 Small 10 264 39 Small 15 157 40 Large 21 719 41 Medium 19 460 42 Small 16 203 43 Medium 26 363 44 Large 19 1052 45 Large 18 1687 46 Small 26 189 47 Medium 18 321 48 Medium 18 521 49 Large 23 1215 50 Medium 13 435 51 Medium 16 428 52 Large 17 1479 53 Medium 30 335 54 Medium 22 681 55 Medium 28 404 56 Small 15 180 57 Medium 14 554 58 Medium 30 612 59 Large 29 1264 60 Large 21 610 61 Small 20 221 62 Small 29 254 63 Medium 19 601 64 Large 15 1026 65 Small 25 293 66 Medium 14 585 67 Small 13 231 68 Medium 14 512 69 Medium 11 513 70 Medium 24 545 71 Medium 33 555 72 Small 13 241 73 Small 8 140 74 Small 11 168 75 Medium 20 644 76 Large 10 707 77 Medium 15 561 78 Medium 20 379 79 Large 14 1484 80 Small 30 177 81 Large 18 1019 82 Medium 27 601 83 Large 25 1420 84 Small 26 210 85 Small 22 251 86 Medium 14 558 87 Medium 22 743 88 Medium 24 620 89 Medium 22 372 90 Large 23 1045 91 Medium 15 671 The Homework 8.xlsx file contains sample data on 91 billings for retail customers of the wholesale operation of Bluth's original Frozen Banana. Data include (i) the size of the customer in three categories, (ii) the number of days it takes the customer to pay their b and (iii) the amount of the bill in dollars. a. The collections manager at Bluth's would like for fewer than half of all orders to take longer than 20 days to be paid. Based on the sample and with 95% confidence, address the collections manager's hypothesis. b. what is the probability of type error for the hypothesis in part b when the proportion p of orders taking longer than 17 days to be paid is actually 0.45?Explanation / Answer
Part a
Here, we have to use the z test for the population proportion.
The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: p = 0.5 versus Alternative hypothesis: Ha: p < 0.5
This is a one tailed (left tailed) test.
We are given
Confidence level = c = 0.95, so, = 1 – 0.95 = 0.05
Sample size = n = 91
X = number of orders taking more than 20 days = 37
Sample proportion = P = X/n = 37/91 = 0.406593
Population proportion = p = 0.50, so q = 1 – p = 1 – 0.50 = 0.50
The test statistic formula is given as below:
Z = (P – p)/sqrt(pq/n)
Z = (0.406593 – 0.50) / sqrt(0.50*0.50/91)
Z = -1.7821
Critical value = -1.6449
P-value = 0.0374
= 0.05
P-value < = 0.05
So, we reject the null hypothesis
This means we conclude that there is sufficient evidence that fewer than half of all orders to take longer than 20 days to be paid.
Part b
Null hypothesis: H0: p = 0.45 versus Alternative hypothesis: Ha: p 0.45
Sample size = n = 91
X = number of orders taking more than 17 days = 56
Sample proportion = P = X/n = 56/91 = 0.615385
Population proportion = p = 0.45, so q = 1 – p = 1 – 0.45 = 0.55
Z = (0.615385 – 0.45)/sqrt(0.45*0.55/91) = 3.171241
P(Z>3.171241) = 1 - 0.999241 = 0.000759
P(Type II) = 0.000759