Exam 8: Large-Sample Estimation

One-sided confidence bounds can be constructed for the population mean and population proportion p, but not for (the difference between population means) or (the difference between population proportions).

A lawn service owner is testing new environmentally friendly weed killers. He discovers that a particular weed killer is effective 89% of the time. Suppose that this estimate was based on a random sample of 60 applications. Construct a 90% confidence interval for p, the true proportion of weeds killed by this particular brand.

An experiment was conducted to compare two diets A and B, designed for weight reduction. Two groups of 50 overweight dieters each were randomly selected. One group was placed on diet A and the other on diet B, and their weight losses were recorded over a 30-day period. The means and standard deviations of the weight-loss measurements (in kg) for the two groups are shown in the table. Find a 95% confidence interval for the difference in mean weight loss for the two diets. Interpret your confidence interval.

Ground Beef Weights Narrative The meat department of a local supermarket packages ground beef using meat trays of two sizes: one designed to hold approximately 700 g of meat, and a larger one that holds approximately 1.4 kg. A random sample of 36 packages of the smaller meat trays produced weight measurements with an average of 715 g and a standard deviation of 90 g. -Refer to Ground Beef Weights Narrative. Suppose that the quality control department of this supermarket chain intends that the amount of ground beef in the smaller trays should be 700 g on average. Should the confidence interval above concern the quality control department? Explain.

An airline executive estimates that 25% of all flights arrive late. How many flights must we include in a simple random sample if we want to be 90% confident that the true population proportion of flights that arrive late lies within 0.01 of our sample proportion? Justify your conclusion.

Given that n = 49, = 75, and = 7, the lower and upper limits of the 68.26% confidence interval for the population mean are 74 and 76, respectively.

Two independent random samples of sizes and have been selected from binomial populations with respective parameters and , resulting in 38 and 65 successes, respectively. Then, the point estimation of the difference is -27.

The error of estimation is the difference between a statistic computed from a sample and the corresponding parameter computed from the population.

The error of estimation is the distance between an estimate and the estimated parameter.

After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. In order to correct this , what should you do?

Random sample of n = 1000 observations from a binomial population produced x = 728 successes. Estimate the binomial proportion p and calculate the margin of error.

One way to reduce the margin of error in a confidence interval is to decrease the confidence coefficient.

Why do those who engage in estimation insist on random sampling, rather than convenience sampling or judgment sampling?

A quality control engineer wants to determine what is the proportion of defective parts coming off the assembly line. Past experiments, based on large sample sizes, have shown this proportion to be 0.19. What sample size does the engineer need in order to estimate, with 90% confidence, this proportion with a margin of error of 0.12? Justify your conclusion.

Which of the following best describes the term "margin of error"?

Two independent random samples of sizes and have been selected from binomial populations with respective parameters and , resulting in 38 and 65 successes, respectively. Then the standard error of is estimated as 0.077.

Increasing the confidence level for a confidence interval estimate for the difference between two population means, with all other things held constant, will result in a wider confidence interval estimate.

A parent believes the average height for 14-year-old girls differs from that of 14-year-old boys. Estimate the difference in height between girls and boys, using a 95% confidence interval. The summary data are listed below. Based on your interval, do you think there is a significant difference between the true mean height of 14-year-old girls and boys? Explain. 14-year-old girls' summary data: = 40, = 155 cm, = 6.1 cm 14-year-old boys' summary data: = 40, = 146 cm, = 9.1 cm

Suppose a 95% confidence interval for the mean height of a 12-year-old male in Canada is 137 to 165 cm. In repeated sampling, 95% of the intervals constructed will contain the interval from 137 to 165 cm.

If we wish to construct a 95% confidence interval estimate for the difference between two population proportions, what would the confidence level be?