Question

The diameters of ball bearings made by a machine follow a normal distribution. Ball bearings that are too large or too small are undesirable since they will not work properly. The manager wants to see if the machine is producing ball bearings that are significantly different from .35 inches. To make sure the machine is working properly, we take a random sample of 25 ball bearings and find that the sample mean diameter is .34 inches. Assume the population standard deviation is.02 inches. which of the following represents a 95% confidence interval for the mean? 02 1.645 2(333, 347) 645 ( )-(343, .357) 1.96 (.02)- (332, 348) V25 02 25 02 d. .35±1.96 e. .34 +2.576 (02 25 25(.330,.351) 02 25 2. Based on the confidence interval, does it appear as if the machine is functioning properly? a. b. c. d. Yes: 95% confidence interval contains .35 Yes: 95% confidence interval contains .34 No: 95% confidence interval contains values both above and below .34 No: 95% confidence interval contains values both above and below .35 No: 95% confidence interval is entirely above .34 No: 95% confidence interval is entirely below .35 3. Which of the following would have led to a narrower confidence interval? Sample mean of.345 inches Population standard deviation of.03 inches Using a 90% level of confidence a. None would have led to a narrower interval b. I C. T only e. Iand II f. and III g. II and III h. I, II, and III only d. III onljy Suppose the true population mean ball bearing size produced by the machine is actually .35. If 80 random samples of ball bearings had been taken and a 95% confidence interval calculated for each, how many of these confidence intervals would we expect to contain.35? 4. b. 4 ?. 40 d. 76 e. 80

Answer 1

1. z value for 95% CI is 1.96 as P(-1.96<z<1.96)=0.95

And formula for CI is $\overline{x}\pm z* \frac{\sigma }{\sqrt{n}}=0.34 \pm 1.96*\frac{0.02}{\sqrt{25}}=(0.332,0.348)$

Hence answer is c.

2. As 0.35 is not in the range correct answer is f.

3. Reducing the confidence level will make the CI narrow

So answer is d. III only

4. It is 76.