STAT 160 Midterm Page 3 Fall 2017 engincer wants to estimate the fraction of def

Question

STAT 160 Midterm Page 3 Fall 2017 engincer wants to estimate the fraction of defectives in a large lot of m previous experience, he feels that the actual proportion of 3. A quality-control cartridgen. file cartrid Sld be somewhere around 0.05. How large a sample should be taken if he an ts to estimate the true fraction to be within 0.01, using a 95% confidence interv Answer: 4. Independent random samples of sizes 14 and n2 5 are se population 1 and normal populatin 2, respectively; -Population 2H1238 5T Population 2 14 7 79 6 (a) Assume that the two populations have a common vari pooled estimate of 2 ance 2, compute sa, the Answer: ) Find the value of the test statistic for testing Ho : 1-2-0 vs. Ha : Answer ind the p-value for the hyp Answer: ed on the p-value in part (c) can we reject Ho? (Yes/No) Answer: sample of n = 7 observations from a normal population produced

Explanation / Answer

3) at 95% confidence the critical value is 1.96

Margin of error = 0.01

Z* * sqrt (p * (1 - p )/n) = 0.01

Or, 1.96 * sqrt(0.05 * 0.95 /n ) = 0.01

Or, (0.05 * 0.95)/n = (0.01/1.96)2

Or, n = (0.05 * 0.95)/(0.01/1.96)2

Or, n = 1824.76 = 1825

4) For population 1

X1 = 7, s1 = 3.92, n1 = 4

For population 2

X2 = 8.6, s2 = 3.21, n2 = 5

A) Pooled variance = ((n1 - 1)s12 + (n2 - 1)s22)/(n1 + n2 - 2)

= (3 * (3.92)^2 + 4 * (3.21)^2)/7

= 12.47 = 12

B) The test statistic t = (x1 - x2)/sqrt(s1^2/n1 + s2^2/n2)

= (7 - 8.6)/sqrt(12/4 + 12/5)

= -0.69

C) DF = 4 + 5 - 2 = 7

P-VALUE = 2 * P(T < -0.69)

= 2 * 0.2562

= 0.5124

D) As the p-value is greater than the alpha value 0.05 so the null hypothesis is not rejected.

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