Question

1. The mean number of days it takes an employer to approve medical leave is believed to be about ten. Members of a collective bargaining unit do not believe this figure. They randomly survey eight employees. The number of days they took to approve medical leave are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Let X = the number of days the employer took to approve medical leave. (a) Identify a null and alternative hypothesis. (b) Determine a decision-making matrix based on choosing to reject or to not reject the null hypothesis. (c) For a 5% level of significance, find the critical value ta (d) Find the t-statistic for the data. (e) Should the collective bargaining unit believe that the mean number is ten? 2. For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Carmichael feels this is not true, so she asked a local college statistics class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. (a) Identify a null and alternative hypothesis. (b) For a a = 0.01 level of significance, find the P-value for your data. (c) Did the class demonstrate that the percentage was higher in Carmichael? 3. University students were recruited for a study of how many words people speak in a day. A random sample of 56 men resulted in a mean of 16,576 words and a standard deviation of 7,871 words. We'll use a a = 0.01 level of significance to test the claim that men have a standard deviation for words that is greater than the standard deviation of 7,460 words for women. (a) Identify a null and alternative hypothesis (b) Apply an appropriate hypothesis test, using either the test statistic comparison or P- value method. Clearly state your conclusion.

Answer 1

0 8.375 200i-2 17.871 h-1 7 S4.1036 Test stcatts Htis 8.375-10 t 4.10/42 s/Nn -1 12)0 b) t-Statts e t-cmti cal al ue hen oe do not rejcet Ho tox nHcal uolue -ta2 344 statistte t - 1.1210 Toneolecthre Here 1t 1 t A CCept Ho The colleotve bargaininy unit bellve that the mear number S ten

So1n a Ho P = 0.67 MIs H P t0.67 (ь) p - 8 2 O82 1 n=100 Po o.67, 1-Po 0-33 test statistHe is Hence b-Po -0.82-0.67 O.67 X0.33 loa Z3.190o PT 2319 0.0014 P-vael u e Here P-value Ldo.05 We Rejeet Ho The class demonstaete that the percentage was not higher in carmicheel

A) Ho (7460)2 6 0 VIS :(6.) 79c02 (b) Given 6= 78 7 1 2(xi-2 2 2 Z Cxi-X (7871) xs6 The test stahstic ts 2Cxi-2 Go 371ס )- xss 2 (746012 22 62.34 PE62.34 .0001 p-val ue Here p-value o.01 Rejeet Ho The men hawe standard deviatien dur rd that is greot er thah than the stemdlard desiation ot 7460 oreds for women