Question

Coffee beans from around the world are used to make coffee. Do coffee tasters prefer coffee beans from particular countries? To investigate this question, a researcher collected coffee aroma ratings based on Arabica coffee beans from two countries, Brazil and Costa Rica. The coffee aroma ratings are summarized in the table below. Each sample contains 10 coffee bean ratings. Sample Standard Deviation n Sample Mean Costa Rica 10 7.74 0.26 Brazil 10 7.54 0.25 We will assume that the aroma ratings of coffees from these two countries are normally distributed. Let's perform a hypothesis test at the 5% significance level. Test that the mean aroma rating of coffee made from Costa Rican coffee beans is greater than the mean aroma rating of coffee made from Brazilian coffee beans. Let Hy be the mean aroma rating of coffee made from Costa Rican coffee beans. And let H2 be the mean aroma rating of coffee made from Brazilian coffee beans. The difference in sample means should be: mean for Costa Rican sample minus mean for Brazilian sample. Compute the T-test statistic? Hint: This is the T-score of the difference in sample means, assuming the null hypothesis is true. Round to two decimal places.

Answer 1

The test statistic is 1.75 t 7.74-7.54 12 10 10 0.26 13²4 N₂ +0.252 The degrees of freedom ti t is $4+39 0.26_0.2522 df 10 0.252 no 1₂. SA n?(n-1) n(n-1) 0.264 + 10²x9. 10²x9 df = 18 Critical Value: t18,0.05. 1.734 since, Our test statistic is greater than the Critical Value. So, we reject to at 5% significance levele Hence, we can support the claim that the aroma rating of coffee made from costa rica coffee beans is greater than the aroma rating of coffee Brazilian coffee beans. mean mean made from

Percentage Points for the t distribution This table gives percentage points x defined by the equation 00 dt P= 1 1(12v+2) TvT (12v) X (1+2+/)%*) Р 0 х The limiting distribution of t as v tends to infinity is the standard normal distribution. When v is large, interpolation in v should be harmonic. P= 40% 30% 25% 20% 15% 10% 5% 2.5% 1% 0.5% 0.1% 0.05% V 1 0.3249 0.7265 1.000 1.376 1.963 3.078 6.314 12.71 31.82 63.66 318.3 636.6 2 0.2887 0.6172 0.8165 1.061 1.386 1.886 2.920 4.303 6.965 9.925 22.33 31.60 3 0.2767 0.5844 0.7649 0.9785 1.250 1.638 2.353 3.182 4.541 5.841 10.21 12.92 4 0.2707 0.5686 0.7407 0.9410 1.190 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 0.2672 0.5594 0.7267 0.9195 1.156 1.476 2.015 2.571 3.365 4.032 5.894 6.869 6 0.2648 0.5534 0.7176 0.9057 1.134 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 0.2632 0.5491 0.7111 0.8960 1.119 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 0.2619 0.5459 0.7064 0.8889 1.108 1.397 1.860 - 2.306 - 2.896 3.355 4.501 5.041 9 0.2610 0.5435 0.7027 0.8834 1.100 1.383 1.833 2.262 2.821 3.250 4.297 4.781 10 0.2602 0.5415 0.6998 0.8791 1.093 1.372 1.812 2.228 2.764 3.169 4.144 4.587 11 0.2596 0.5399 0.6974 0.8755 1.088 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 0.2590 0.5386 0.6955 0.8726 1.083 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 0.2586 0.5375 0.6938 0.8702 1.079 1.350 1.771 2.160 2.650 3.0123.852 4.221 14 0.2582 0.5366 0.6924 0.8681 1.076 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 0.2579 0.5357 0.6912 0.8662 1.074 1.341 1.753 2.131 2.602 2.947 3.733 4.073 16 0.2576 0.5356 0.6901 0.8647 1.071 1.337 1.746 2.120 2.583 2.921 3.686 4.015 17 0.2573 0.5344 0.6892 0.8633 1.069 1.333 1.740 2.110 2.567 2.898 3.646 3.965 18 0.2571 0.5338 0.6884 0.8620 1.067 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 0.2569 0.5333 0.6876 0.8610 1.066 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 0.2567 0.5329 0.6870 0.8600 1.064 1.325 1.725 2.086 2.528 2.845 3.552 3.850 21 0.2566 0.5325 0.6864 0.8591 1.063 1.323 1.721 2.080 2.518 2.831 3.527 3.819 22 0.2564 0.5321 0.6858 0.8583 1.061 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 0.2563 0.5317 0.6853 0.8575 1.060 1.319 1.714 2.069 2.500 2.807 3.485 3.768 24 0.2562 0.5314 0.6848 0.8569 1.059 1.318 1.711 2.064 2.492 2.797 3.467 3.745 25 0.2561 0.5312 0.6844 0.8562 1.058 1.316 1.708 2.060 2.485 2.787 3.450 3.725 26 0.2560 0.5309 0.6840 0.8557 1.058 1.315 1.706 2.056 2.479 2.779 3.435 3.707 27 0.2559 0.5306 0.6837 0.8551 1.057 1.314 1.703 2.052 2.473 2.771 3.421 3.689 28 0.2558 0.5304 0.6834 0.8546 1.056 1.313 1.701 2.048 2.467 2.763 3.408 3.674 29 0.2557 0.5302 0.6830 0.8542 1.055 1.311 1.699 2.045 2.462 2.756 3.396 3.660 30 0.2556 0.5300 0.6828 0.8538 1.055 1.310 1.697 2.042 2.457 2.750 3.385 3.646 32 0.2555 0.5297 0.6822 0.8530 1.054 1.309 1.694 2.037 2.449 2.738 3.365 3.622- 34 0.2553 0.5294 0.6818 0.8523 1.052 1.307 1.691 2.032 2.441 2.728 3.348 3.601 36 0.2552 0.5291 0.6814 0.8517 1.052 1.306 1.688 2.028 2.434 2.719 3.333 3.582 38 0.2551 0.5288 0.6810 0.8512 1.051 1.304 1.686 2.024 2.429 2.712 3.319 3.566 40 0.2550 0.5286 0.6807 0.8507 1.050 1.303 1.684 2.021 2.423 2.704 3.307 3.551 50 0.2547 0.5278 0.6794 0.8489 1.047 1.299 1.676 2.009 2.403 2.678 3.261 3.496 60 0.2545 0.5272 0.6786 0.8477 1.045 1.296 1.671 2.000 2.390 2.660 3.232 3.460 120 0.2539 0.5258 0.6765 0.8446 1.041 1.289 1.658 1.980 2.358 2.617 3.160 3.373 0.2533 0.5244 0.6745 0.8416 1.036 1.282 1.645 1.960 2.326 2.576 3.090 3.291