Exam 11: Estimation: Describing a Single Population

A sample of size 200 is to be taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion will be greater than 0.58 is: A. 0.281. B. 0.719 C. 0.580. D. 0.762.

In developing an interval estimate for a population mean, the interval estimate was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was: A. 56.34. B. 62.96. C. 13.24. D. 66.15.

An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger.

Which of the following best describes an unbiased estimator? A Every estimator is an unbiased estimator. B An interval estimator is an unbiased estimator. C An unbiased estimator of a population parameter is an estimator whose expected value is equal to that parameter. D None of these choices are correct.

A normal population has a standard deviation of 15. How large a sample should be drawn to estimate the population mean to within 1.5 with 95% confidence?

When constructing a confidence interval estimate of $\mu$ , doubling the sample size n reduces the width %of the interval by half.

The larger the level of confidence used in constructing a confidence interval, the wider the confidence interval.

A confidence interval becomes narrower as the sample size increases, for the same percentage of confidence.

The width of a confidence interval estimate of the population mean widens when the: A level of confidence increases. B sample size increases. C population standard deviation decreases. D Sample mean gets further from the population mean.

Find and interpret a 98% confidence interval for the mean number of animals visited by a veterinarian per day. A random sample of 35 veterinarians, found that they had a sample mean of 25.3 animals and a sample variance of 2.8 animals.

Under which of the following circumstances is it impossible to construct a confidence interval for the population mean? A A non-normal population with a large sample and an unknown population variance. B A normal population with a large sample and a known population variance. C A non-normal population with a small sample and an unknown population variance. D A normal population with a small sample and an unknown population variance.

In developing an interval estimate at 87.4% for a population mean, the value of z to use is: A. 1.15. B. 0.32. C. 1.53. D. 0.16.

Find and interpret a 95% confidence interval for the population mean number of laptops owned by an average Australian household, if a random sample of 40 Australian households had a sample mean of 1.3 laptops. The population variance is known to be 4 laptops².

Which of the following statistical distributions is used when estimating the population mean when the population variance is known? A Student t distribution B Standard normal distribution C Chi-square distribution D None of these choices are correct.

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use with a 99% confidence level?

An interval estimate is a range of values within which the actual value of a population parameter $\mu$ falls.

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal: A. 77.769 B. 72.231 C. 72.727 D. 77.273

A sample of 50 students was asked how much time they spend on average a week in front of a computer. The sample mean and sample standard deviation were 15.8 and 2.7 hours, respectively. Estimate with 95% confidence interval the mean number of hours students spend in front of a computer a week.

Which of the following statements is false? A The t -distribution is symmetric about zero. B The t -distribution is more spread out than the standard normal distribution. C As the number of degrees of freedom gets smaller, the t -distribution's dispersion gets smaller. D The t -distribution is mound-shaped.

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours. Determine the 95% confidence interval estimate of the population mean, changing the population standard deviation to 1.2.