Question

3. Suppose that we are testing Ho: u = 80 vs. Ha: u <80 at the .05 level and we are going to collect 10 pieces of data and o=1.2. Determine the probability of Type Il error for the alternative kl. = 79.25. ANSWER 4. Company A claims that their tires outlast the tires of Company B by more than 12.000 miles. We feel certain that Il = 62,000 ,- 5,100. Data for Company A is collected and summarized: Company A n=15 F= 76,300 s=4800. Perform an a =.05 level test. Ho: Test Statistic Ha: Conclusion:

Answer 1

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3)

Probability of type 2 error = 0.698541350944464

4)

H_{​​​​​​0} : population mean = 62000

H_{​​​​​​a} : population mean > 62000

Test Statistic : 11.53826289

Conclusion : We have sufficient evidence to Rejecting null hypothesis and conclude that the claim of Company A may be true.

Pnoba bility of type 1 erroY P(Rajecting Ho to is true Caven) O.05 P (Accepting to P(tyee error pR andh srond is true

n 1o therefore Here can use t clistri bution of freedlong to calculate the probability dgre with test staatishic 80 P(type Ierror P( 17 1-2/16 O.05 19 from t table uoith freedom 9 dlegree of O0 -1.8.33 -80 17 79 3044254

P(type T error -P C79.3044 2541 1-2/o 79-25 PCO.014 342854 698541350944464

49 Ho 6 2 000 62000 HA Test statistics - 76 300 -62000 4 8005 11.53826289 statistic Test 17 it fodlows t cistaibutto with free dlom Erog elagree of 14 t tabte ८गंतकव Vवो fडु 7-761

Calculateel T value lti 588 s areater than Table value 1.76 17 have sufficient eridence to Reject the null hypothesis and we concluole the clain of is true may company