# Construct a confidence interva

Construct a confidence interval for

μd​, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed.

A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a​ 95% confidence interval for the mean difference between the before and after scores. Round to the nearest tenth.

Before After
74      73
83      77
75      70
88      77
84      74
63      67
93      95
84      83
91      84
77      75

# Construct a confidence interva

Of 346 items tested, 12 are found to be defective. Construct the 98% confidence interval for the proportion of all such items that are defective.

How do you convert the numbers to equate like this: 0.0345<p<0.0349

# Construct a Confidence Interva

A survey of 300 union members in New York reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate.

# Construct a Confidence Interva

Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. Quality control personnel inspect a random sample of the teams assemblies and judge each assembly to be acceptable or unacceptable. A random sample of 127 assemblies from team 1 shows 12 unacceptable assemblies. A similar random sample of 98 assemblies from team 2 shows 5 unacceptable assemblies.

a. Construct a 90% confidence interval for the difference between the portions of unacceptable assemblies generated by the two teams.

b. Based on a review of the confidence interval found in part a, is there sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their portions of unacceptable assemblies. Conduct a hypothesis test to prove this theorem.

c. For which values of the differences between these two sample portions could you conclude that a statistically significant difference exists? (at ? = .10 level)

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