Question

In: Statistics and Probability

1) A) A point estimate: is a single value estimate for a population [ Select ]...

1)

A) A point estimate: is a single value estimate for a population [ Select ] ["statistic", "parameter"] .

To estimate the population mean [ Select ] ["µ", "x-bar"] we use the sample mean [ Select ] ["µ", "x-bar"] .

To estimate the population proportion [ Select ] ["p", "p-hat"] we use the sample proportion [ Select ] ["p", "p-hat"] .

B)

The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean in which of the following conditions (select all that apply):

if the sample size is reasonably large (for any population).

if the population is Normally distributed and the sample size is reasonably large.

if the population is Normally distributed (for any sample size).

if the sample data is normally distributed.

C)

A random sample of 50 bottles of a particular brand of cough medicine is selected and the alcohol content of each bottle is determined. Let μ denote the average alcohol content for the population of all bottles of the brand under study. The 95% confidence interval for is μ (7.8, 9.4).

  1. A 90% confidence interval would be [ Select ] ["narrower", "wider"] than the 95% interval given.
  2. If the sample size was increased to 100, the confidence interval would be [ Select ] ["narrower", "wider"] than the given interval.

  3. "We are 95% confident” means [ Select ] ["There is a 95% probability that the interval contains the true mean.", "There is a 95% chance that the interval contains the sample mean.", "This interval was constructed using a method that produces intervals that capture the true mean in 95% of all possible samples"] .

D)

A significance test about a proportion is conducted using a significance level of 0.05. The sample statistic is p-hat = 0.12. The p-value is 0.03.

  1. What conclusion would you make for this test? [ Select ] ["Reject Ho", "Fail to reject Ho"]
  2. If this test resulted in a decision error, what type of error was it? [ Select ] ["Type I", "Type II"]

Solutions

Expert Solution

A)

A point estimate: is a single value estimate for a population parameter.

To estimate the population mean µ we use the sample mean x-bar.

To estimate the population proportion p we use the sample proportion p-hat.

B)

The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean

if the sample size is reasonably large (for any population).

if the population is Normally distributed (for any sample size).

C)

  1. A 90% confidence interval would be narrower than the 95% interval given.
  2. If the sample size was increased to 100, the confidence interval would be narrower than the given interval.

  3. "We are 95% confident” means This interval was constructed using a method that produces intervals that capture the true mean in 95% of all possible samples

D)

Given that significance level = 0.05. p-value is 0.03.

If p-value is less than significance level, we Reject Ho.

  1. What conclusion would you make for this test? Reject Ho
  2. If this test resulted in a decision error, what type of error was it? Type I

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