Need help with the following problem. Lifesaver rating for firstcorrect answer.

Question

Need help with the following problem. Lifesaver rating for firstcorrect answer.

A manufacturer of gas filters had numerous complaints. They did aquality check with a sample of 600 filters (200 per shift). Theinspection produced the following results:

SHIFT                           DEFECTIVE ITEMS
1st                                  25
2nd       35
3rd    80

a. Does the data indicate that the quality of the filters isrelated to the shift producing them? Test using =.05

b. Estimate the proportion of defective filters produced by thefirst shift. Use a 95% confidence interval.    

Explanation / Answer

Null hypothesis : Quality and Shift areindependent. Alternative Hypothesis : Quality and Shift are dependent. SHIFT                           DEFECTIVE ITEMS   Prop.Def.inshiftwise      Estimate
1st                                  25                                          25/200=0.125      23
2nd      35                                          35/200=0.175      23
3rd    80                                          80/200= 0.4       23 Chi-Square (Test ) statistic = (O-E)2/E                                           = 0.1739+6.26+141.26 = 147.6
Chi-Square value at 3-1 = 2 degrees of freedom at 0.05is 5.99 (use Statistical tables ) We reject the Null hypothesis . So data indicate thatthe quality of the filters is related to the shift producingthem Proportion of defective in first shift =0.125 95% confidence interval = 0.125±1.96*(0.125*0.875)/200 Simplify Hope this helps you

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