Exam 8: Large-Sample Estimation

A laboratory technician is interested in the proportion of 1 litre containers used in the lab that are glass. How many containers should be sampled in order to estimate, with 99% confidence, this proportion with a margin of error of less than 0.2? Justify your conclusion.

The sample proportion is an unbiased estimator of the population proportion, p.

Suppose you wish to estimate the difference between two population means when the population variances are known. Which critical values of z can you use to develop the 90% confidence interval estimate?

A sample statistic such that the mean of all its possible values equals the population parameter that the statistic seeks to estimate is an unbiased estimator.

From a sample of 200 items, 12 items are defective. In this case, what will be the point estimate of the population proportion defective?

Number of Salon Hair Colourings Narrative A stylist at the Hair Care Palace gathered data on the number of hair colourings given on Saturdays and on weekdays. Her results are listed below. Assume the two random samples were independently taken from normal populations. Saturday: = 50 and = 14 Weekday: = 65 and = 13 -Refer to Number of Salon Hair Colourings Narrative. Find the point estimate of p₁ - p₂ and the margin of error.

The margin of error equals the sum of an estimator's squared bias plus its variance.

NBA Series Narrative A TV pollster believed that 70% of all TV households would be tuned in to Game 6 of the 2009 NBA Championship series between the LA Lakers and the Orlando Magic. A random sample of 500 TV households was selected and 365 indicated they were tuned into the game. -Refer to NBA Series Narrative. Based on the interval in the previous question, can the pollster's claim be rejected? Justify your answer.

Telephone Poll Radio and television stations often air controversial issues during broadcast time and ask viewers to indicate their agreement or disagreement with a given stand on the issue. A poll is conducted by asking those viewers who agree to call a certain 900 telephone number and those who disagree to call a second 900 telephone number. All respondents pay a fee for their calls. -Please refer to Telephone Poll paragraph. Does this polling technique result in a random sample?

A manufacturer wishes to estimate the mean time a battery pack will function before needing to be recharged, with a margin of error of no more than 0.5 hours and with probability 0.95. If the standard deviation is known to be 1.5 hours, how many observations should be included in the sample? Justify your conclusion.

A random sample of 45 salespersons were asked how long, on average, they were able to talk to a potential customer. Their answers revealed a mean of 8.5 minutes with a variance of 9 minutes. Construct a 95% confidence interval for , the time it takes an salesperson to talk to a potential customer.

In order to estimate the average number of kilometres that students living off-campus commute to classes every day, the following statistics were given: n = 50, = 5.21, and s = 2.48. Which of the values below would be the best point estimate of the true population mean ?

An estimator is a random variable calculated from a random sample that provides either a point estimate or an interval estimate for some population parameter.

As the sample size increases and other factors remain the same, the width of a confidence interval for a population mean tends to decrease.

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. Construct a 99% confidence interval for the average weight of all packages sold in the smaller meat trays by this supermarket.

The standard error of the sampling distribution of is given by the formula SE =

Suppose you wish to estimate a population mean based on a sample of n observations. What sample size is required if you want your estimate to be within 2 standard deviations of with probability equal to 0.95, if you know the population standard deviation is 12?

A random sample of 400 students was surveyed to determine an estimate for the proportion of all students who had attended at least three football games. The estimate revealed that between 0.372 and 0.458 of all students attended. Given this information, which of the following is the approximate value of the confidence coefficient?

A point estimate is an estimate of the range of a population parameter.

Laptop Batteries Narrative A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the two models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent random samples and computed the following summary information: -Refer to Laptop Batteries Narrative. Find Based on the interval in the previous question, can one conclude there is a difference in the true average functioning time before recharging between the two models of battery packs? Justify your answer.