Question

1)
Out of 100 people sampled, 60 preferred Candidate A. Based on this, estimate what proportion of the voting population (pp) prefers Candidate A.

Use a 99% confidence level, and give your answers as decimals, to three places.

_____ < P < ______

2)

You work for a marketing firm that has a large client in the automobile industry. You have been asked to estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned to gather a random sample that could be used to estimate this proportion to within a 0.015 margin of error at a 90% level of confidence.

a) With no prior research, what sample size should you gather in order to obtain a 0.015 margin of error? Round your answer up to the nearest whole number.

n = ____ households

b) Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required. You conduct a small preliminary sample, and you obtain a sample proportion of ˆp=0.185p^=0.185 . Using this new information. what sample size should you gather in order to obtain a 0.015 margin of error? Round your answer up to the nearest whole number.

n = ___ households

3)

You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of ¯x=74x¯=74 hours with a standard deviation of s=7s=7 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.75 hours at a 90% level of confidence.

What sample size should you gather to achieve a 0.75 hour margin of error? Round your answer up to the nearest whole number.

n = ____ bacteria

4)

ou want to estimate the average weight in tons of loads carried by trucks through a particular stretch of road. From previous information the standard deviation is expected to be σ=16.1 tons. How many trucks must be weighed to estimate the the tons per truck to within 5 tons at a 98% level of confidence. Round your answer up to the largest whole number.

n = ____ trucks

5)
Assume that a sample is used to estimate a population mean μμ. Find the 80% confidence interval for a sample of size 47 with a mean of 73.8 and a standard deviation of 6.8. Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

80% C.I. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1