Test equally likeliness of random numbers

Question

Assignment:

1) Test equally likeliness of random numbers.

a. Use Excel to generate 500 random digits per the instructions below.

2. In the bottom of the dialog box enter 0 and in the top enter, then click OK. This tells Excel to generate digits between 0 and 9.

3. Highlight cells A1 through A500 so you get 500 digits generated.

4. You can record these results in a table such as you did previously for a histogram with the Excel "bin" feature. In column B enter the values 0-9 in
the first 10 rows. How use Histogram in Data Analysis to generate a
frequency table to better see the results.

b. Use a significance level of 0.05 to test the claim that your sample of digits come from a population where all digits are equally likely. Report on whether or not Excel is properly generating random numbers. Make sure to show all our work in the submitted spreadsheet.

2) Test for the same mean. See at the attached Words.xls data file for this part of the project.

a. Test the null hypothesis that the six samples of word counts for males (odd columns ending in M) are from a population with the same mean.

b. Test the null hypothesis that the six samples of word counts for females (even columns) are from a population with the same mean.

c. If we want to compare the number of words spoken by men to the number spoken by women, does it make sense to combine the six columns to word counts for males and the same for females before then comparing?

d. Make a report that addresses each of parts a-c above and justify your answers.

3) Testing Random Numbers by nonparametic methods.

a. Use the random numbers created in part 1) above and test for randomness using three of the methods in chapter 13. Again, show all work and report on the findings of each.

4) Quality control process testing. Again, use the RANDBETWEEN function in Excel. This time generate 200 random numbers between 1 and 100 and output it to one column. Then do the same for until you have 20 columns of which are 200 in length that all have values between 1 and 100.

a. The above generated data is to simulate 20 days of a quality control process. Consider an outcome of 1-5 to be a defect and an outcome of 6-100 to be an acceptable result. Note that this corresponds to a 5% rate of defects.

b. Construct a p chart for the proportion of defective calculators, and determine whether the process is within statistical control. The process is stable with p = 0.05 so a conclusion that it is not stable would be a type I error which means we would have a false positive signal causing use to think that the process should be adjusted when, in fact, it was fine.

c. Simulate another 10 days of manufacturing calculators (as in part a), but modify these 10 so that the defect rate is 10% instead of 5%.

d. Combine the data from parts a) an c) to represent a total of 30 days of results. Construct a p chart for this combined sample. Is the process out of control or not? If we conclude it is not, we would make a type II error which means that we would believe the process was fine when it should be adjusted to correct the 10% rate of defects.

e. Again, make all your data presentable and report on your findings.

1M	1F	2M	2F	3M	3F	4M	4F	5M	5F	6M	6F
27531	20737	23871	16109	21143	6705	47016	11849	39207	15962	28408	15357
15684	24625	5180	10592	17791	21613	27308	25317	20868	16610	10084	13618
5638	5198	9951	24608	36571	11935	42709	40055	18857	22497	15931	9783
27997	18712	12460	13739	6724	15790	20565	18797	17271	5004	21688	26451
25433	12002	17155	22376	15430	17865	21034	20104		10171	37786	12151
8077	15702	10344	9351	11552	13035	24150	17225		31327	10575	8391
21319	11661	9811	7694	11748	24834	24547	14356		8758	12880	19763
17572	19624	12387	16812	12169	7747	22712	20571			11071	25246
26429	13397	29920	21066	15581	3852	20858	12240			17799	8427
21966	18776	21791	32291	23858	11648	3189	10031			13182	6998
11680	15863	9789	12320	5269	25862	10379	13260			8918	24876
10818	12549	31127	19839	12384	17183	15750	22871			6495	6272
12650	17014	8572	22018	11576	11010	4288	26533			8153	10047
21683	23511	6942	16624	17707	11156	12398	26139			7015	15569
19153	6017	2539	5139	15229	11351	25120	15204			4429	39681
1411	18338	36345	17384	18160	25693	7415	18393			10054	23079
20242	23020	6858	17740	22482	13383	7642	16363			3998	24814
10117	18602	24024	7309	18626	19992	16459	21293			12639	19287
20206	16518	5488	14699	1118	14926	19928	12562			10974	10351
16874	13770	9960	21450	5319	14128	26615	15422			5255	8866
16135	29940	11118	14602		10345	21885	29011				10827
20734	8419	4970	18360		13516	10009	17085				12584
7771	17791	10710	12345		12831	35142	13932				12764
6792	5596	15011	17379		9671	3593	2220				19086
26194	11467	1569	14394		17011	15728	5909				26852
10671	18372	23794	11907		28575	19230	10623				17639
13462	13657	23689	8319		23557	17108	20388				16616
12474	21420	11769	16046		13656	23852	13052
13560	21261	26846	5112		8231	11276	12098
18876	12964	17386	8034		10601	14456	19643
13825	33789	7987	7845		8124	11067	21747
9274	8709	25638	7796			18527	26601
20547	10508	695	20910			11478	17835
17190	11909	2366	8756			6025	14030
10578	29730	16075	5683			12975	7990
14821	20981	16789	8372			14124	16667
15477	16937	9308	17191			22942	5342
10483	19049		8380			12985	12729
19377	20224		16741			18360	18920
11767	15872		16417			9643	24261
13793	18717		2363			8788	8741
5908	12685		24349			7755	14981
18821	17646					9725	1674
14069	16255					11033	20635
16072	28838					10372	16154
16414	38154					16869	4148
19017	25510					16248	5322
37649	34869					9202
17427	24480					11395
46978	31553
25835	18667
10302	7059
15686	25168
10072	16143
6885	14730
20848	28117