# Cub Foods - Inferential Statistics, Question 3

```Bertha Weaver, James Wooley, Mary Songer, Bill Jones
Math 113 - 01: Spring 2000
```

# Is the mean price of Cub Foods significantly different from each of the other stores?

```There is no signficant difference in Cubs and Eagles, except with respect to Breakfast Cereals, where Cubs is significantly cheaper, both for the regular price and the sale price.
```

```There is no signficant difference in Cubs and Krogers, except with respect to Breakfast Cereals and Soups and Sauces, where Cubs is significantly cheaper, both for the regular price and the sale price.
```

```There is no signficant difference in Cubs and Schnucks, except with respect t
Breakfast Cereals, where Cubs is significantly cheaper, but only for the discounte
price.
```

```There is no signficant difference in Cubs and WalMart.
```

```It appears that there is no overall significant difference between Cu
Foods and any of the other stores, although Cubs appears to be cheape
than everybody except WalMart on Breakfast Cereals.
```

# Cubs vs Eagles

Group Statistics

Store Name N Mean Std. Deviation Std. Error Mean
Regular Price Cubs 37 2.2759 1.4443 .2374
Eagles 37 2.3562 1.4612 .2402
Price Paid Cubs 37 2.0630 1.3446 .2210
Eagles 37 2.2811 1.4194 .2333

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference
Regular Price Equal variances assumed .037 .849 -.238 72 .813 -8.0270E-02 .3378
Equal variances not assumed

-.238 71.990 .813 -8.0270E-02 .3378
Price Paid Equal variances assumed .411 .524 -.679 72 .500 -.2181 .3214
Equal variances not assumed

-.679 71.790 .500 -.2181 .3214

Group Statistics
Product Category Store Name N Mean Std. Deviation Std. Error Mean
Dairy Products Regular Price Cubs 3 3.6100 1.0923 .6307
Eagles 3 3.6233 1.4572 .8413
Price Paid Cubs 3 3.5067 1.2163 .7022
Eagles 3 3.6233 1.4572 .8413
Beverages Regular Price Cubs 6 3.1333 2.4901 1.0166
Eagles 6 2.7450 2.4304 .9922
Price Paid Cubs 6 2.4433 2.4398 .9960
Eagles 6 2.7450 2.4304 .9922
Breakfast Cereals Regular Price Cubs 8 2.9138 .4557 .1611
Eagles 8 3.3713 .5345 .1890
Price Paid Cubs 8 2.5338 .4613 .1631
Eagles 8 3.0738 .6079 .2149
Snacks and Sweets Regular Price Cubs 5 2.2520 1.0946 .4895
Eagles 5 2.0400 1.2440 .5563
Price Paid Cubs 5 2.1740 1.0962 .4903
Eagles 5 1.9600 1.1530 .5157
Fruits and Fruit Juices Regular Price Cubs 5 1.7240 .9895 .4425
Eagles 5 1.8500 .9762 .4366
Price Paid Cubs 5 1.7240 .9895 .4425
Eagles 5 1.8500 .9762 .4366
Lunch Meat Regular Price Cubs 4 1.0400 .3000 .1500
Eagles 4 1.0900 .6000 .3000
Price Paid Cubs 4 1.0400 .3000 .1500
Eagles 4 1.0900 .6000 .3000
Soups and Sauces Regular Price Cubs 4 .7625 .1972 9.860E-02
Eagles 4 1.0200 .2322 .1161
Price Paid Cubs 4 .7625 .1972 9.860E-02
Eagles 4 1.0200 .2322 .1161
Meats Regular Price Cubs 2 2.0900 1.1314 .8000
Eagles 2 2.4900 .7071 .5000
Price Paid Cubs 2 2.0900 1.1314 .8000
Eagles 2 2.4900 .7071 .5000

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference
Product Category
Dairy Products Regular Price Equal variances assumed .552 .499 -.013 4 .990 -1.3333E-02 1.0514
Equal variances not assumed

-.013 3.708 .991 -1.3333E-02 1.0514
Price Paid Equal variances assumed .254 .640 -.106 4 .920 -.1167 1.0959
Equal variances not assumed

-.106 3.876 .920 -.1167 1.0959
Beverages Regular Price Equal variances assumed .011 .918 .273 10 .790 .3883 1.4205
Equal variances not assumed

.273 9.994 .790 .3883 1.4205
Price Paid Equal variances assumed .045 .836 -.215 10 .834 -.3017 1.4059
Equal variances not assumed

-.215 10.000 .834 -.3017 1.4059
Breakfast Cereals Regular Price Equal variances assumed .070 .796 -1.842 14 .087 -.4575 .2483
Equal variances not assumed

-1.842 13.658 .087 -.4575 .2483
Price Paid Equal variances assumed 1.871 .193 -2.002 14 .065 -.5400 .2698
Equal variances not assumed

-2.002 13.054 .067 -.5400 .2698
Snacks and Sweets Regular Price Equal variances assumed .276 .614 .286 8 .782 .2120 .7410
Equal variances not assumed

.286 7.873 .782 .2120 .7410
Price Paid Equal variances assumed .081 .783 .301 8 .771 .2140 .7115
Equal variances not assumed

.301 7.980 .771 .2140 .7115
Fruits and Fruit Juices Regular Price Equal variances assumed .004 .949 -.203 8 .844 -.1260 .6216
Equal variances not assumed

-.203 7.999 .844 -.1260 .6216
Price Paid Equal variances assumed .004 .949 -.203 8 .844 -.1260 .6216
Equal variances not assumed

-.203 7.999 .844 -.1260 .6216
Lunch Meat Regular Price Equal variances assumed 1.800 .228 -.149 6 .886 -5.0000E-02 .3354
Equal variances not assumed

-.149 4.412 .888 -5.0000E-02 .3354
Price Paid Equal variances assumed 1.800 .228 -.149 6 .886 -5.0000E-02 .3354
Equal variances not assumed

-.149 4.412 .888 -5.0000E-02 .3354
Soups and Sauces Regular Price Equal variances assumed .782 .411 -1.690 6 .142 -.2575 .1523
Equal variances not assumed

-1.690 5.846 .143 -.2575 .1523
Price Paid Equal variances assumed .782 .411 -1.690 6 .142 -.2575 .1523
Equal variances not assumed

-1.690 5.846 .143 -.2575 .1523
Meats Regular Price Equal variances assumed 1688918582536988.000 .000 -.424 2 .713 -.4000 .9434
Equal variances not assumed

-.424 1.678 .720 -.4000 .9434
Price Paid Equal variances assumed 1688918582536988.000 .000 -.424 2 .713 -.4000 .9434
Equal variances not assumed

-.424 1.678 .720 -.4000 .9434

# Cubs vs Krogers

Group Statistics

Store Name N Mean Std. Deviation Std. Error Mean
Regular Price Cubs 37 2.2759 1.4443 .2374
Krogers 37 2.4359 1.4702 .2417
Price Paid Cubs 37 2.0630 1.3446 .2210
Krogers 37 2.3078 1.3838 .2275

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference
Regular Price Equal variances assumed .001 .978 -.472 72 .638 -.1600 .3388
Equal variances not assumed

-.472 71.977 .638 -.1600 .3388
Price Paid Equal variances assumed .369 .546 -.772 72 .443 -.2449 .3172
Equal variances not assumed

-.772 71.941 .443 -.2449 .3172

Group Statistics
Product Category Store Name N Mean Std. Deviation Std. Error Mean
Dairy Products Regular Price Cubs 3 3.6100 1.0923 .6307
Krogers 3 3.6567 1.1719 .6766
Price Paid Cubs 3 3.5067 1.2163 .7022
Krogers 3 3.6567 1.1719 .6766
Beverages Regular Price Cubs 6 3.1333 2.4901 1.0166
Krogers 6 2.9400 2.4704 1.0085
Price Paid Cubs 6 2.4433 2.4398 .9960
Krogers 6 2.5900 2.1991 .8978
Breakfast Cereals Regular Price Cubs 8 2.9138 .4557 .1611
Krogers 8 3.4425 .5250 .1856
Price Paid Cubs 8 2.5338 .4613 .1631
Krogers 8 3.3175 .4644 .1642
Snacks and Sweets Regular Price Cubs 5 2.2520 1.0946 .4895
Krogers 5 2.1300 .9535 .4264
Price Paid Cubs 5 2.1740 1.0962 .4903
Krogers 5 1.5580 .7197 .3219
Fruits and Fruit Juices Regular Price Cubs 5 1.7240 .9895 .4425
Krogers 5 1.9320 1.2713 .5686
Price Paid Cubs 5 1.7240 .9895 .4425
Krogers 5 2.4100 1.0803 .4831
Lunch Meat Regular Price Cubs 4 1.0400 .3000 .1500
Krogers 4 1.0150 .4500 .2250
Price Paid Cubs 4 1.0400 .3000 .1500
Krogers 4 .7975 .5950 .2975
Soups and Sauces Regular Price Cubs 4 .7625 .1972 9.860E-02
Krogers 4 1.0400 .1023 5.115E-02
Price Paid Cubs 4 .7625 .1972 9.860E-02
Krogers 4 1.0400 .1023 5.115E-02
Meats Regular Price Cubs 2 2.0900 1.1314 .8000
Krogers 2 2.7250 9.192E-02 6.500E-02
Price Paid Cubs 2 2.0900 1.1314 .8000
Krogers 2 2.5750 .1202 8.500E-02

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference
Product Category
Dairy Products Regular Price Equal variances assumed .033 .865 -.050 4 .962 -4.6667E-02 .9249
Equal variances not assumed

-.050 3.980 .962 -4.6667E-02 .9249
Price Paid Equal variances assumed .000 .987 -.154 4 .885 -.1500 .9752
Equal variances not assumed

-.154 3.994 .885 -.1500 .9752
Beverages Regular Price Equal variances assumed .040 .845 .135 10 .895 .1933 1.4320
Equal variances not assumed

.135 9.999 .895 .1933 1.4320
Price Paid Equal variances assumed .026 .876 -.109 10 .915 -.1467 1.3409
Equal variances not assumed

-.109 9.894 .915 -.1467 1.3409
Breakfast Cereals Regular Price Equal variances assumed .015 .905 -2.151 14 .049 -.5288 .2458
Equal variances not assumed

-2.151 13.728 .050 -.5288 .2458
Price Paid Equal variances assumed .120 .734 -3.387 14 .004 -.7838 .2314
Equal variances not assumed

-3.387 13.999 .004 -.7838 .2314
Snacks and Sweets Regular Price Equal variances assumed .092 .769 .188 8 .856 .1220 .6492
Equal variances not assumed

.188 7.852 .856 .1220 .6492
Price Paid Equal variances assumed .478 .509 1.050 8 .324 .6160 .5865
Equal variances not assumed

1.050 6.908 .329 .6160 .5865
Fruits and Fruit Juices Regular Price Equal variances assumed 1.844 .212 -.289 8 .780 -.2080 .7205
Equal variances not assumed

-.289 7.545 .781 -.2080 .7205
Price Paid Equal variances assumed .003 .958 -1.047 8 .326 -.6860 .6552
Equal variances not assumed

-1.047 7.939 .326 -.6860 .6552
Lunch Meat Regular Price Equal variances assumed .692 .437 .092 6 .929 2.500E-02 .2704
Equal variances not assumed

.092 5.227 .930 2.500E-02 .2704
Price Paid Equal variances assumed 1.764 .232 .728 6 .494 .2425 .3332
Equal variances not assumed

.728 4.433 .503 .2425 .3332
Soups and Sauces Regular Price Equal variances assumed .847 .393 -2.498 6 .047 -.2775 .1111
Equal variances not assumed

-2.498 4.506 .060 -.2775 .1111
Price Paid Equal variances assumed .847 .393 -2.498 6 .047 -.2775 .1111
Equal variances not assumed

-2.498 4.506 .060 -.2775 .1111
Meats Regular Price Equal variances assumed 10137733791678280.000 .000 -.791 2 .512 -.6350 .8026
Equal variances not assumed

-.791 1.013 .572 -.6350 .8026
Price Paid Equal variances assumed 9593526692860800.000 .000 -.603 2 .608 -.4850 .8045
Equal variances not assumed

-.603 1.023 .653 -.4850 .8045

# Cubs vs Schnucks

Group Statistics

Store Name N Mean Std. Deviation Std. Error Mean
Regular Price Cubs 37 2.2759 1.4443 .2374
Schnucks 37 2.4062 1.4057 .2311
Price Paid Cubs 37 2.0630 1.3446 .2210
Schnucks 37 2.3414 1.3129 .2158

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference
Regular Price Equal variances assumed .043 .837 -.393 72 .695 -.1303 .3313
Equal variances not assumed

-.393 71.947 .695 -.1303 .3313
Price Paid Equal variances assumed .201 .655 -.901 72 .371 -.2784 .3090
Equal variances not assumed

-.901 71.959 .371 -.2784 .3090

Group Statistics
Product Category Store Name N Mean Std. Deviation Std. Error Mean
Dairy Products Regular Price Cubs 3 3.6100 1.0923 .6307
Schnucks 3 3.4900 1.1000 .6351
Price Paid Cubs 3 3.5067 1.2163 .7022
Schnucks 3 3.0567 1.3317 .7688
Beverages Regular Price Cubs 6 3.1333 2.4901 1.0166
Schnucks 6 3.0383 2.2367 .9131
Price Paid Cubs 6 2.4433 2.4398 .9960
Schnucks 6 2.8717 1.8944 .7734
Breakfast Cereals Regular Price Cubs 8 2.9138 .4557 .1611
Schnucks 8 3.3138 .4930 .1743
Price Paid Cubs 8 2.5338 .4613 .1631
Schnucks 8 3.3138 .4930 .1743
Snacks and Sweets Regular Price Cubs 5 2.2520 1.0946 .4895
Schnucks 5 2.5260 1.0823 .4840
Price Paid Cubs 5 2.1740 1.0962 .4903
Schnucks 5 2.5260 1.0823 .4840
Fruits and Fruit Juices Regular Price Cubs 5 1.7240 .9895 .4425
Schnucks 5 1.6520 1.0619 .4749
Price Paid Cubs 5 1.7240 .9895 .4425
Schnucks 5 2.1300 1.0065 .4501
Lunch Meat Regular Price Cubs 4 1.0400 .3000 .1500
Schnucks 4 1.2900 .5831 .2915
Price Paid Cubs 4 1.0400 .3000 .1500
Schnucks 4 1.2900 .5831 .2915
Soups and Sauces Regular Price Cubs 4 .7625 .1972 9.860E-02
Schnucks 4 .8225 .2311 .1156
Price Paid Cubs 4 .7625 .1972 9.860E-02
Schnucks 4 .8225 .2311 .1156
Meats Regular Price Cubs 2 2.0900 1.1314 .8000
Schnucks 2 2.2400 1.0607 .7500
Price Paid Cubs 2 2.0900 1.1314 .8000
Schnucks 2 .9950 .7000 .4950

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference
Product Category
Dairy Products Regular Price Equal variances assumed .046 .841 .134 4 .900 .1200 .8950
Equal variances not assumed

.134 4.000 .900 .1200 .8950
Price Paid Equal variances assumed .100 .768 .432 4 .688 .4500 1.0413
Equal variances not assumed

.432 3.968 .688 .4500 1.0413
Beverages Regular Price Equal variances assumed .230 .642 .070 10 .946 9.500E-02 1.3665
Equal variances not assumed

.070 9.887 .946 9.500E-02 1.3665
Price Paid Equal variances assumed .122 .735 -.340 10 .741 -.4283 1.2611
Equal variances not assumed

-.340 9.422 .742 -.4283 1.2611
Breakfast Cereals Regular Price Equal variances assumed .011 .919 -1.685 14 .114 -.4000 .2374
Equal variances not assumed

-1.685 13.914 .114 -.4000 .2374
Price Paid Equal variances assumed .066 .801 -3.267 14 .006 -.7800 .2387
Equal variances not assumed

-3.267 13.938 .006 -.7800 .2387
Snacks and Sweets Regular Price Equal variances assumed .023 .883 -.398 8 .701 -.2740 .6884
Equal variances not assumed

-.398 7.999 .701 -.2740 .6884
Price Paid Equal variances assumed .029 .869 -.511 8 .623 -.3520 .6889
Equal variances not assumed

-.511 7.999 .623 -.3520 .6889
Fruits and Fruit Juices Regular Price Equal variances assumed .138 .720 .111 8 .914 7.200E-02 .6491
Equal variances not assumed

.111 7.960 .914 7.200E-02 .6491
Price Paid Equal variances assumed .048 .831 -.643 8 .538 -.4060 .6312
Equal variances not assumed

-.643 7.998 .538 -.4060 .6312
Lunch Meat Regular Price Equal variances assumed 10.371 .018 -.762 6 .475 -.2500 .3279
Equal variances not assumed

-.762 4.484 .484 -.2500 .3279
Price Paid Equal variances assumed 10.371 .018 -.762 6 .475 -.2500 .3279
Equal variances not assumed

-.762 4.484 .484 -.2500 .3279
Soups and Sauces Regular Price Equal variances assumed .121 .740 -.395 6 .707 -6.0000E-02 .1519
Equal variances not assumed

-.395 5.855 .707 -6.0000E-02 .1519
Price Paid Equal variances assumed .121 .740 -.395 6 .707 -6.0000E-02 .1519
Equal variances not assumed

-.395 5.855 .707 -6.0000E-02 .1519
Meats Regular Price Equal variances assumed 22978007067400.980 .000 -.137 2 .904 -.1500 1.0966
Equal variances not assumed

-.137 1.992 .904 -.1500 1.0966
Price Paid Equal variances assumed 1745685012672260.000 .000 1.164 2 .365 1.0950 .9408
Equal variances not assumed

1.164 1.668 .384 1.0950 .9408

# Cubs vs WalMart

Group Statistics

Store Name N Mean Std. Deviation Std. Error Mean
Regular Price Cubs 37 2.2759 1.4443 .2374
WalMart 37 1.9876 1.2638 .2078
Price Paid Cubs 37 2.0630 1.3446 .2210
WalMart 37 1.9222 1.2856 .2114

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference
Regular Price Equal variances assumed 1.233 .271 .914 72 .364 .2884 .3155
Equal variances not assumed

.914 70.754 .364 .2884 .3155
Price Paid Equal variances assumed .011 .915 .460 72 .647 .1408 .3058
Equal variances not assumed

.460 71.856 .647 .1408 .3058

Group Statistics
Product Category Store Name N Mean Std. Deviation Std. Error Mean
Dairy Products Regular Price Cubs 3 3.6100 1.0923 .6307
WalMart 3 2.7767 1.1082 .6398
Price Paid Cubs 3 3.5067 1.2163 .7022
WalMart 3 2.7767 1.1082 .6398
Beverages Regular Price Cubs 6 3.1333 2.4901 1.0166
WalMart 6 2.6083 2.1530 .8789
Price Paid Cubs 6 2.4433 2.4398 .9960
WalMart 6 2.6083 2.1530 .8789
Breakfast Cereals Regular Price Cubs 8 2.9138 .4557 .1611
WalMart 8 2.5125 .7576 .2679
Price Paid Cubs 8 2.5338 .4613 .1631
WalMart 8 2.5125 .7576 .2679
Snacks and Sweets Regular Price Cubs 5 2.2520 1.0946 .4895
WalMart 5 1.9720 1.1050 .4942
Price Paid Cubs 5 2.1740 1.0962 .4903
WalMart 5 1.9720 1.1050 .4942
Fruits and Fruit Juices Regular Price Cubs 5 1.7240 .9895 .4425
WalMart 5 1.6680 .9373 .4192
Price Paid Cubs 5 1.7240 .9895 .4425
WalMart 5 1.1840 .8606 .3849
Lunch Meat Regular Price Cubs 4 1.0400 .3000 .1500
WalMart 4 .9300 .5000 .2500
Price Paid Cubs 4 1.0400 .3000 .1500
WalMart 4 .9300 .5000 .2500
Soups and Sauces Regular Price Cubs 4 .7625 .1972 9.860E-02
WalMart 4 .7650 .2042 .1021
Price Paid Cubs 4 .7625 .1972 9.860E-02
WalMart 4 .7650 .2042 .1021
Meats Regular Price Cubs 2 2.0900 1.1314 .8000
WalMart 2 2.2400 1.0465 .7400
Price Paid Cubs 2 2.0900 1.1314 .8000
WalMart 2 2.2400 1.0465 .7400

Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference
Product Category
Dairy Products Regular Price Equal variances assumed .006 .940 .928 4 .406 .8333 .8984
Equal variances not assumed

.928 3.999 .406 .8333 .8984
Price Paid Equal variances assumed .054 .828 .768 4 .485 .7300 .9500
Equal variances not assumed

.768 3.966 .485 .7300 .9500
Beverages Regular Price Equal variances assumed .266 .617 .391 10 .704 .5250 1.3439
Equal variances not assumed

.391 9.796 .704 .5250 1.3439
Price Paid Equal variances assumed .025 .877 -.124 10 .904 -.1650 1.3284
Equal variances not assumed

-.124 9.848 .904 -.1650 1.3284
Breakfast Cereals Regular Price Equal variances assumed .284 .603 1.284 14 .220 .4012 .3126
Equal variances not assumed

1.284 11.478 .225 .4012 .3126
Price Paid Equal variances assumed .195 .665 .068 14 .947 2.125E-02 .3136
Equal variances not assumed

.068 11.563 .947 2.125E-02 .3136
Snacks and Sweets Regular Price Equal variances assumed .003 .959 .403 8 .698 .2800 .6956
Equal variances not assumed

.403 7.999 .698 .2800 .6956
Price Paid Equal variances assumed .001 .973 .290 8 .779 .2020 .6961
Equal variances not assumed

.290 7.999 .779 .2020 .6961
Fruits and Fruit Juices Regular Price Equal variances assumed .006 .939 .092 8 .929 5.600E-02 .6095
Equal variances not assumed

.092 7.977 .929 5.600E-02 .6095
Price Paid Equal variances assumed .075 .792 .921 8 .384 .5400 .5865
Equal variances not assumed

.921 7.849 .385 .5400 .5865
Lunch Meat Regular Price Equal variances assumed 1.059 .343 .377 6 .719 .1100 .2915
Equal variances not assumed

.377 4.912 .722 .1100 .2915
Price Paid Equal variances assumed 1.059 .343 .377 6 .719 .1100 .2915
Equal variances not assumed

.377 4.912 .722 .1100 .2915
Soups and Sauces Regular Price Equal variances assumed .004 .955 -.018 6 .987 -2.5000E-03 .1419
Equal variances not assumed

-.018 5.993 .987 -2.5000E-03 .1419
Price Paid Equal variances assumed .004 .955 -.018 6 .987 -2.5000E-03 .1419
Equal variances not assumed

-.018 5.993 .987 -2.5000E-03 .1419
Meats Regular Price Equal variances assumed 67556743301479.700 .000 -.138 2 .903 -.1500 1.0898
Equal variances not assumed

-.138 1.988 .903 -.1500 1.0898
Price Paid Equal variances assumed 67556743301479.700 .000 -.138 2 .903 -.1500 1.0898
Equal variances not assumed

-.138 1.988 .903 -.1500 1.0898