Question

A businesswoman is considering whether to open a coffee shop in a local shopping center. Before making this decision, she wants to know how much money people spend per week at coffee shops in that area. She took a random sample of 26 customers from the area who visit coffee shops and asked them to record the amount of money in dollars) they would spend during the next week at coffee shops. At the end of the week, she obtained the following data in dollars) from these 26 customers 16.84 39.13 15.28 14.38 5.01 63.57 10.15 13.28 32.31 36.00 16.20 65.99 10.13 37.02 3.21 6.80 34.72 6.41 36.31 27.6138.53 13.30 9.69 9.44 1.23 5.27 Assume that the distribution of weekly expenditures at coffee shops by all customers who visit coffee shops in this area is approximately normal. Round your answers to cents. a. What is the point estimate of the corresponding population mean? T$ 2134 b. Make a 98% confidence interval for the average amount of money spent per week at coffee shops by all customers who visit coffee shops in this area. $ 29.79 to $ 1390

Answer 1

We have given that data of 26 customers. (Sample) 14.38 16.84 13.28 3.21 39.13 32.31 15.28 36 10.15 37.02 16.20 6.41 5.01 63.57 65.gg 10.13 36.31 27.61 5.27 38.53 34.72 9.44 13.30 9.69 1.23 mean of sample=Sum of all observations Total number of obsesvations - 16.84 +39.13 & 15.28+ +5.27 26 567.81 26 2825 21.8388 mean of Sample Population mean mean of sample 21.8388 X = $ 21.84 26 6 variance of sample. & xin n-1 Scanned ----------

+(5.27 - 21.84 = 16.84 -21.84) + (39:13.-21.84) + 26-1 7888.05 25 52 315.52 (given that 1-2 - 98% 1-0 =0.98 f = 0.02 Test statistic, tead - X - M ntny of Sun-T By defination of confidence Interval, ana) Rin 1-d. nol L M to incl) - 98% sluni asher n-1 = to 0.02, 26-1 2 tool, 25 = 2.48511 (t-table rolue CamScanner

2.4 4851) L 21.84- 41 (2.48511 98% => PC- 17.76) 726-1 > p (-2. = 98% 2.48511 21.84-rl < 2.48511 3.552 >> p (-8.83 < (21.84-41) € 8.83 98% 98% > p (-8.83 - 21.84 < 6-4) § 8.83 -21.54 & pl. 29.7 t 4) I > p (-30.67 % (-4) 3-13.0)) - 98% - = 7 p ( 13.01 € 2 80.67 = 98% The 98% confidence interval is, $ 13.01 to $ 30.67 Scanned with CamScanner

Numbers in each row of the table are values on a t-distribution with (df) degrees of freedom for selected right-tail (greater-than) probabilities (p). Х t (p. df) df/p 0.005 1 2 3 4 0.10 3.077684 1.885618 1.637744 1.533206 1.475884 1.439756 1.414924 1.396815 0.0005 636.6192 31.5991 12.9240 8.6103 6.8688 5.9588 5.4079 5.0413 5 6 7 8 9 4.7809 10 4.5869 11 12 0.40 0.324920 0.288675 0.276671 0.270722 0.267181 0.264835 0.263167 0.261921 0.260955 0.260185 0.259556 0.259033 0.258591 0.258213 0.257885 0.257599 0.257347 0.257123 0.256923 0.256743 0.256580 0.256432 0.256297 266172 0.25 1.000000 0.816497 0.764892 0.740697 0.726687 0.717558 0.711142 0.706387 0.702722 0.699812 0.697445 0.695483 0.693829 0.692417 0.691197 0.690132 0.689195 0.688364 0.687621 0.686954 0.686352 0.685805 0.685306 GO1050 0.05 6.313752 2.919986 2.353363 2.131847 2.015048 1.943180 1.894579 1.859548 1.833113 1.812461 1.795885 1.782288 1.770933 1.761310 1.753050 1.745884 1.739607 1.734064 1.729133 1.724718 1.720743 1.717144 1.713872 1.710002 0.025 12.7062 4.30269 3.18245 2.77649 2.57058 2.44691 2.36462 2.30600 2.26216 2.22814 2.2009 2.17881 2.16031 2.14479 2.13149 2.11991 2.10982 2.10092 2.09302 2.08596 2.07961 2.07381 2.06866 200200 0.01 31.82052 6.96456 4.54070 3.74695 3.36493 3.14267 2.99795 2.89646 2.82144 2.76377 2.71808 2.68100 2.65031 2.62449 2.60248 2.58349 2.56693 2.55238 2.53948 2.52798 2.51765 2.50832 2.49987 2.10214 1.383029 1.372184 1.363430 1.356217 1.350171 1.345030 1.340606 1.336757 1.333379 1.330391 1.327728 1.325341 1.323188 1.321237 1.319460 1217026 13 14 15 16 63.65674 9.92484 5.84091 4.60409 4.03214 3.70743 3.49948 3.35539 3.24984 3.16927 3.10581 3.05454 3.01228 2.97684 2.94671 2.92078 2.89823 2.87844 2.86093 2.84534 2.83136 2.81876 2.80734 2.79694 2.78744 2.77871 2.77068 2.76326 2.75639 2.75000 2.57583 99% 17 18 19 20 21 4.4370 43178 4.2208 4.1405 4.0728 4.0150 3.9651 3.9216 3.8834 3.8495 3.8193 3.7921 3.7676 3.7454 3.7251 3.7066 3.6896 3.6739 3.6594 3.6460 3.2905 99.9% 22 23 25 2.48511 26 0.256060 0.255955 0.255858 1.316345 1.314972 1.313703 1.312527 2.05954 2.05553 2.05183 2.47003 2.47266 27 28 0.684430 0.684043 0.683685 0.683353 0.683044 0.682756 0.674490 1.708141 1.705618 1.703288 1.701131 1.699127 1.697261 1.644854 90% 0.255768 0.255684 0.255605 0.253347 2.46714 2.46202 29 2.04841 2.04523 2.04227 1.95996 1.311434 1.310415 1.281552 30 2.45726 2.32635 Z CI 80% 95% 98%