High Fashion Boutiques
High Fashion Boutiques
Statistics help please can anyone help me with this?
4. A group of young businesswomen wish to open a high fashion boutique in a vacant store, but only if the average income of households in the area is at least $45,000. A random sample of 15 households showed the following results.
$47,000 $48,000 $48,000 $44,000 $46,000
$42,000 $43,000 $45,000 $43,000 $47,000
$46,000 $48,000 $46,000 $44,000 $42,000
Use statistical techniques to advise the group on whether or not they should locate the boutique in this store. Use a .05 level of significance.
The first attempt at defining hypotheses:
H0: Mean income >= $45,000
HA: Mean income < $45,000
But the above is a problem. It says that we will assume that mean income is at least $45,000, unless there is very good evidence otherwise. That is hardly what we want. We should be assuming that income is less than necessary, unless there is very good evidence otherwise.
I'm not sure whether this is just a simple question and you should just blindly follow the procedure, or whether you are expected to recognize the problem. I'll assume you should see the problem.
There are a couple of things you could do. One is to design the test to avoid Type II errors instead of Type I, but that isn't generally taught in basic courses. The simpler is just to change the hypotheses:
H0: Mean income <= $45,000
H1: Mean income > $45,000
Which seems very different, but there is actually very little difference between “at least” and “greater than.” In fact, presuming we could find the exact average income, the only difference would be if the average income was exactly $45,000.
But with these hypotheses, we insist that the data convince us. That is, the mean of our sample will have to be significantly higher than $45,000 in order to convince us that the population mean is at least $45,000 — exactly what we want. So:
Mean = $45,267
Standard deviation = $2,154
Standard error = SD/sqrt(n) = $2,154/sqrt(15) = $556
The test statistic t = ($45,267 – $45,000) / $556 = .48
The critical value for a one-tailed test at the .05 level of significance with (sample size – 1 = 15-1 =) 14 degrees of freedom (from a t table) is 1.761.
Since the test statistic does not exceed the critical value, we do not reject the null hypothesis and we must presume that the local mean income is less than or equal to $45,000.
Sounds like a no to me. And with such a small difference in means and small standard deviation, it would take a sample size on the order of 300 to be comfortable otherwise.
My Favorite Minnesota – Shopping – Shoes Fashion Sales
|
|
WIRE MANNEQUIN Store Boutique Display High Fashion 62″ $155.00 |
|
|
Selection of 80′s high Quality Jewellery/Jewelry,Exclusive Fashion Boutique Lot $7.88 |
|
|
NWT Funky Hawaii Shirt For High Fashion Kids Boutique $15.59 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Black Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Black Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Black Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Black Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Black Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Black Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Black Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Black Glitter boutique37 $29.00 |
|
|
♥BOUTIQUE STYLE♥ SEXY HIGH FASHION BLACK FEATHER GOLD TONE CHAIN LINK EARRINGS $8.99 |
|
|
♥BOUTIQUE♥ HIGH FASHION BROWN BUBBLY FRINGED SUPER SOFT RUCHED SCARF $12.99 |
|
|
♥BOUTIQUE♥ HIGH FASHION LEOPARD CHEETAH ZEBRA PRINT FRINGED SOFT SCARF $14.99 |
|
|
♥BOUTIQUE STYLE♥ FAB HIGH FASHION MINI BLACK BEAD CLUSTER GOLD TONE EARRINGS $9.99 |
|
|
ROOTSTEIN MANNEQUINS FOR HIGH END FASHION BOUTIQUES $449.00 |
|
|
Boutique 2 Way Carry High Fashion Handbags Purses Must Have For Styling 4 Colors $23.99 |
|
|
Boutique 2 Way Carry High Fashion Handbags Purses Must Have For Styling 4 Colors $23.99 |
|
|
Boutique 2 Way Carry High Fashion Handbags Purses Must Have For Styling 4 Colors $23.99 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Gold Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Gold Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Gold Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Gold Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Gold Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Gold Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Gold Glitter boutique37 $29.00 |
|
|
NEW BAMBOO Women Fashion Work High Heel Party Pump sz Gold Glitter boutique37 $29.00 |
|
|
Puppy In My Pocket Fashion Boutique – High Street $14.20 |
|
|
Vintage Advertising RENATA BOUTIQUE Italy High Fashion $14.95 |
|
|
Boutique 9 Women’s ‘Wendell’ Brown High Heels $48.99 Slip into style with these lovely brown suede, pointed-toe heels from Boutique 9. A 4.5-inch tapered heel and a 1-inch platform complete these absolutely stunning high heels. |
|
|
Boutique 9 Women’s ‘Wendell’ Grey High Heels $69.99 Slip into style with these lovely grey suede, pointed-toe heels from Boutique 9. A 4.5-inch tapered heel and a 1-inch platform complete these absolutely stunning high heels. |
|
|
JoJo Designs Black and White Jacquard Handbag $32.99 Carry your belongings in style with this chic handbag by JoJo DesignsBag is constructed using only high quality materialsStylish accessory features boutique designer fabric and grosgrain ribbon trim |
|
|
JoJo Designs Blue/ Chocolate Jacquard Handbag $32.99 Carry your belongings in style with this chic handbag by JoJo DesignsBag is constructed using only high quality materialsStylish accessory features boutique designer fabric and grosgrain ribbon trim |
|
|
Shoe Done It (Paperback) $6.92 Rita Jewel has a dream job selling fabulous clothes and accessories to the socialites of San Francisco at Dolce`s Boutique. But when a pair of heels becomes a clue in a murder, Rita finds herself engaged in a high- end crime of fashion. |
|
|
JoJo Designs Pink/ Chocolate Brown Damask Print Tote Bag $32.99 JoJo handbag is constructed using high-quality materialsTote bag features exquisite boutique designer fabric and grosgrain ribbon trimBeautiful bag is made of chocolate brown and pink jacquard cotton fabric |
|
|
Spectacular Wineries of the Napa Valley $23.37 From high-end, cult wineries—whose interiors have rarely been seen—to smaller, more accessible vineyards, this series surveys the legends and lore of various locales. Large-scale photographic essays … |
Comments are closed for this entry.