Question

A grad student is reading a research paper in which a hypothesis test on the population average u was performed. The paper claims that their experimental data had a large sample size and it reports a p-value of 0.0044. If the paper states that it used a two-tailed test, then what was the value of their observed test statistic? You may assume that the test statistic is a positive number. Give your answer with the decimal accuracy of our stats tables. Answer:

Answer 1

Ans : Given claim that their experimental data had a large sample size and it reports a p-value of 0.0044

Given that we perform the Two tailed test .

here we know that the experimental data has large sample size

then we perform the Two tailed z test for population mean

To Test :

H0= µ = µ0 versus   H1 : µ ≠ µ0

Test Statistics :

Χ– μο Z σ vn

To find test statistic value :

here we have to given that p value = 0.0044

We know that from the two tailed test

p - value = 2*P(Z > z)

$\Rightarrow$2*P(Z > z) = 0.0044

$\Rightarrow$P(Z > z) = 0.0022

then z = 2. 85 ( From statistical table )

Ans :

Test Statistic = 2.85

TABLE 1 : THE NORMAL PROBABILITY INTEGRAL 0. 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1. 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5. 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 0.02 0 50000 46017 42074 38209 34458 30854 27425 24196 21186 18406 15866 13567 11507 96800 80757 66807 54799 44565 35930 28717 22750 17864 13903 10724 81975 62097 46612 34670 25551 18658 13499 96760 68714 48342 33693 23263 15911 10780 72348 48096 31671 20658 13346 85369 54125 33977 21125 13008 79333 47918 49601 45620 41683 37828 34090 30503 27093 23885 20897 18141 15625 13350 11314 95098 79270 65522 53699 43633 35148 28067 22216 17429 13553 10444 79763 60366 45271 33642 24771 18071 13062 93544 66367 46648 32481 22405 15310 10363 69483 46148 30359 19783 12769 81627 51685 32414 20133 12386 75465 45538 2 49292 45224 41294 37448 33724 30153 26763 23576 20611 17879 15386 13136 11123 93418 77804 64255 52616 42716 34380 27429 21692 17003 13209 10170 77603 58677 43965 32641 24012 17502 12639 90426 64095 45009 31311 21577 14730 99611 66726 44274 29099 18944 12215 78015 49350 30920 19187 11792 71779 43272 3 48803 44828 40905 37070 33360 29806 26435 23270 20327 17619 15151 12924 10935 91759 76359 63008 51551 41815 33625 26803 21178 16586 12874 99031 75494 57031 42692 31667 23274 16948 12228 87403 61895 43423 30179 20778 14171 95740 64072 42473 27888 18138 11685 74555 47117 29492 18283 11226 68267 41115 4 48405 44433 40517 36693 32997 29460 26109 22965 20045 17361 14917 12714 10749 90123 74934 61780 50503 40930 32884 26190 20675 16177 12545 96419 73436 S5426 41453 30720 22557 16411 11829 84474 59765 41889 29086 20006 13632 92010 61517 40741 26726 17365 11176 71241 44979 28127 17420 10686 54920 39061 5 48006 44038 40129 36317 32636 291 16 25785 22663 19766 17106 14686 12507 10565 88508 73529 60571 49471 40059 32157 25588 20182 15778 12224 93867 71428 53861 40246 29798 21860 15889 11442 81635 57703 40406 28029 19262 13112 88417 59059 39076 25609 16624 10689 68069 42935 26823 16597 10171 61731 37107 6 47608 43644 39743 35942 32276 28774 25463 22363 19489 16853 14457 12302 10383 86915 72145 59380 48457 39204 31443 24998 19699 13386 11911 91375 69469 52336 39070 28901 21182 13382 11067 78885 55706 38971 27009 18543 12611 84957 56694 37475 24536 15912 10221 65031 40980 25577 15810 96796 58693 7 47210 43251 39358 35569 31918 28434 25143 22065 19215 16602 14231 12100 10204 85343 70781 58208 47460 38364 30742 24419 19226 15003 11604 88940 67557 50849 37926 28028 20524 14890 10703 76219 53774 37584 26023 17849 12128 81624 54418 35936 23507 15230 97736 62123 39110 24386 15060 92113 55799 33476 8 46812 42858 38974 35197 31561 28096 24825 21770 18943 16354 14007 11900 10027 83793 69437 57053 46479 37538 30054 23852 18763 14629 11304 86563 65691 49400 36811 27179 19884 14412 10350 73638 51904 36243 25071 17180 11662 78414 52228 34458 22518 4575 93447 59340 37322 23249 14344 $7648 53043 31792 9 46414 42465 38591 34827 31207 27760 24510 21476 11673 16109 13786 11702 96325 $2264 68112 55917 45514 36727 29379 23295 18309 14262 11011 14242 63872 472198 35726 26354 19262 13949 10008 71136 50094 34946 24151 16534 11213 75324 S01 22 33037 21569 13940 19337 56675 35612 22162 13660 13391 50418 30190 0.03 0.04 0.05 0.06 35247