Researchers studied the friction that occurs in the paper-feeding process of a p

Question

Researchers studied the friction that occurs in the paper-feeding process of a photocop In a stack of 100 sheets of paper, the feeding process was successful 94 times. The success of the feeder is designed to be .90. Test to determine if the success rate of the feeder .90 at alpha = 0.05. Test statistic Z = p^- p_0/squareroot p_0 middot (1 - p_0)/n and Confidence Interval p^plusminus z_a/2 squareroot p^q^/n State the null and alternative hypothesis. State your conclusion for your hypothesis test. Give the 95% Confidence Interval. Give a conclusion for the confidence interval test.

Explanation / Answer

H0 = null hypothesis is = success rate of feeder is 0.9;
H1 = alternative hypothsis is = success rate of feeder is not 0.9

P0 = 0.9
p= 94/10 = 0.94;
Hence test static z = 0.94-0.9 / (0.9*0.1/100)1/2 = 0.04* 10 / 0.3 = 1.333

for alpha = 0.05 in 2 tail test, z should like between [-1.96,1.96] in this case z= 1.33 so it lies in this range;
Hence we accept the numm hypothesis that success rate of feeder is 0.9

95% confidence itnerval is = p +/- alpha/2 * (p*(1-p)/n)1/2 = 0.94 +- 1.96 * ( 0.94*0.06/100)1/2
= 0.94+- 1.96*0.02374 = 0.94 +- 0.0465 = 0.8935 to 0.9865;
Also notice that 0.9 falls in this range;

Thus the conclusion of confidence interval tests states that with 95% level of certainty we can say that the range of feeding process's success will be in [0.8935, 0.9865]

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.