For the following claim, find the null and alternative hypotheses, test statisti
ID: 3216894 • Letter: F
Question
For the following claim, find the null and alternative hypotheses, test statistic, critical value, and draw a conclusion. Assume that a simple random sample has been selected from a normally distributed population. Answer parts a-d. Claim: The mean IQ score of statistics professors is less than 118. Sample data: n=18, x=113, s=11. The significance level is alpha=0.05 t distribution:
a) Choose the correct null hypothesis (Ho) and alternative hypothesis (H1).
b) Determine the test statistic t using the following formula. Enter the known information into the expression.
c) Find the critical value using a t-distribution table. Look in the row corresponding to n1=9 degrees of freedom and the column corresponding to =.05. Remember that if the test is left-tailed, the critical value will be negative.
Critical t values
Area in One Tail
0.005 0.01 0.025 0.05 0.10
Degrees of Freedom Area in Two Tails
0.01 0.02 0.05 0.10 0.20
1 63.657 31.821 12.706 6.314 3.078
2 9.925 6.965 4.303 2.920 1.886
3 5.841 4.541 3.182 2.353 1.638
4 4.604 3.747 2.776 2.132 1.533
5 4.032 3.365 2.571 2.015 1.476
6 3.707 3.143 2.447 1.943 1.440
7 3.499 2.998 2.365 1.895 1.415
8 3.355 2.896 2.306 1.860 1.397
9 3.250 2.821 2.262 1.833 1.383
10 3.169 2.764 2.228 1.812 1.372
11 3.106 2.718 2.201 1.796 1.363
12 3.055 2.681 2.179 1.782 1.356
13 3.012 2.650 2.160 1.771 1.350
14 2.977 2.624 2.145 1.761 1.345
15 2.947 2.602 2.131 1.753 1.341
16 2.921 2.583 2.120 1.746 1.337
17 2.898 2.567 2.110 1.740 1.333
18 2.878 2.552 2.101 1.734 1.330
19 2.861 2.539 2.093 1.729 1.328
20 2.845 2.528 2.086 1.725 1.325
21 2.831 2.518 2.080 1.721 1.323
22 2.819 2.508 2.074 1.717 1.321
23 2.807 2.500 2.069 1.714 1.319
24 2.797 2.492 2.064 1.711 1.318
25 2.787 2.485 2.060 1.708 1.316
26 2.779 2.479 2.056 1.706 1.315
27 2.771 2.473 2.052 1.703 1.314
28 2.763 2.467 2.048 1.701 1.313
29 2.756 2.462 2.045 1.699 1.311
30 2.750 2.457 2.042 1.697 1.310
31 2.744 2.453 2.040 1.696 1.309
32 2.738 2.449 2.037 1.694 1.309
33 2.733 2.445 2.035 1.692 1.308
34 2.728 2.441 2.032 1.691 1.307
35 2.724 2.438 2.030 1.690 1.306
36 2.719 2.434 2.028 1.688 1.306
37 2.715 2.431 2.026 1.687 1.305
38 2.712 2.429 2.024 1.686 1.304
39 2.708 2.426 2.023 1.685 1.304
40 2.704 2.423 2.021 1.684 1.303
45 2.690 2.412 2.014 1.679 1.301
50 2.678 2.403 2.009 1.676 1.299
60 2.660 2.390 2.000 1.671 1.296
70 2.648 2.381 1.994 1.667 1.294
80 2.639 2.374 1.990 1.664 1.292
90 2.632 2.368 1.987 1.662 1.291
100 2.626 2.364 1.984 1.660 1.290
200 2.601 2.345 1.972 1.653 1.286
300 2.592 2.339 1.968 1.650 1.284
400 2.588 2.336 1.966 1.649 1.284
500 2.586 2.334 1.965 1.648 1.283
1000 2.581 2.330 1.962 1.646 1.282
2000 2.578 2.328 1.961 1.646 1.282
Large 2.576 2.326 1.960 1.645 1.282
Degrees of Freedom Area in One Tail
0.005 0.01 0.03 0.05 0.10
Area in Two Tails
0.01 0.02 0.05 0.10 0.20
Explanation / Answer
1) H0 : mu >= 118
Ha : mu <118
2) x = 113 , s = 11 , n = 18
t = ( x - mu) / (s/sqrt(n))
= ( 113 - 118) / ( 11/sqrt(18))
= -1.93
3) Critical value using t distribution and df = 18 - 1 = 17 and alpha = 0.05
critical value = -1.740