Question

The accompanying data give the sales volume​ (in dollars per square​ foot) for 86 retail outlets specializing in​ women's clothing in 2015 and 2016. Did sales change by a statistically significant amount from 2015 to​ 2016? Use alpha = 0.05.

Let μ1 be the mean sales volume in 2015 and let μ2 be the mean sales volume in 2016.

The​ 95% confidence interval for μd = μ1 − μ2 is ____ to ___ dollars per square foot. ​(Round to two decimal places as​ needed.)

Sales 2015   Sales 2016
405.79   440.47
485.68   514.69
425.27   460.52
418.66   451.47
517.8   593.29
529.65   516.11
448.89   418.84
541.1   545.92
433.02   418.74
397.32   394.67
550.69   665.72
497.76   534.01
399.07   386.68
502.35   471.28
507.7   565.39
390.71   424.21
606.64   664.62
530.05   582.11
416.03   391.76
584.33   599.27
363.4   371.12
497.47   473.85
387.64   452.33
554.28   575.16
519.62   701.9
450.05   426.66
568.29   635.54
535.18   522.68
351.88   387.11
453.17   480.21
541.14   583.66
464.63   484.6
425.84   416.01
438.85   521.08
543.08   566.59
384.85   390.51
391.3   394.46
440.12   440.82
401.79   437.41
514.16   548.34
349.91   380.7
553.55   534.79
550.58   507.05
428.28   412.05
555.49   527.3
364.3   430.25
365.19   439.93
435.01   409.61
493.31   547.36
416.87   376.82
369.66   457.59
555.69   534.73
529.85   572.94
541.95   584.3
436.09   453.18
434.91   502.27
377.21   398.07
366.31   431.55
546.77   621.25
414.15   443.76
471.58   442.99
494.9   486.81
417.93   376.88
483.46   512.04
422.52   387.99
469.08   508.58
565.92   618.51
472.97   459.61
365.35   443.1
467.74   474.41
657.18   677.01
378.75   340.93
499.52   486.21
583.03   586.01
439.94   472.25
544.02   591.83
491.51   402.41
335.71   381.56
453.56   441.36
472.47   503.27
510.5   551.73
399.35   391.41
504.17   486.98
451.28   393.74
468.76   486.61
447.07   480.8

Answer 1

Here we have paired data so paired t test will be used.

Following is the output of paired t test generated by excel:

The required confidence interval is (-28.00, -9.94).

Since confidence interval does not contain zero so sales changed by a statistically significant amount from 2015 to​ 2016 at 0.05 level of significance.