STATS FINAL EXAM CONCEPTS

Why is it correct to say "a" normal distribution and "the" standard normal distribution?

"The" standard normal distribution is used to describe one specific normal distribution (μ=0, σ=1). "A" normal distribution is used to describe a normal distribution with any mean and standard deviation.

Describe the relationship between quartiles and percentiles

(1) Quartiles are special cases of (2) percentiles (3) Q1 is the 25th percentile, (4) Q2 is the 50th percentile, and (5) Q3 is the 75th percentile.

What is the total area under the normal curve?

1

You are applying for a job at two companies. Company A offers starting salaries with μ=$35,000 and σ=$4,000. Company B offers starting salaries with μ=$35,000 and σ= $9,000. From which company are you likely to get an offer of $43,000 or more?

Company B, because data values that lie within one standard deviation from the mean are considered very usual

Determine whether the statement is true of false. If false, rewrite it as a true statement. - As the size of a sample increases, the mean of the distribution of sample means increases.

False. As the size of a sample increases, the mean of the distribution of sample means does not change.

What are some benefits of using graphs of frequency distributions?

It can be easier to identify patterns of a data set by looking a graph of the frequency distribution

From a random sample of 50 business days, gold prices had a mean of $1378.15. Assume the population standard deviation is $203.40. This creates a 90% confidence interval for the population mean of ($1330.84, $1425.46). Does it seem possible that the population mean could equal the sample mean exactly? Explain.

It would be very unlikely because the margin of error is large enough that odds of selecting an exact value is very low.

In a normal distribution, which is greater, the mean or the median? explain.

Neither; in a normal distribution, the mean and median are equal.

From a random sample of 64 dates, the mean record high daily temperature in a certain city has a mean of 84.67°F. Assume the population standard deviation is 14.15°F. This creates a 95% confidence interval for the population mean of (81.20,88.14). Does it seem possible that the population mean could be greater that 89°F? Explain.

No, it does not seem possible because 89°F is greater than the right endpoint of the confidence interval.

You construct a 95% confidence interval for a population mean using a random sample. The confidence interval is 24.9 < μ < 31.5. Is the probability that μ is in this interval 0.95? explain

No. With 95% confidence, the mean is in the interval (24.9, 31.5)

What are some benefits of representing data sets using frequency distributions?

Organizing the data into a frequency distribution can make patterns within the data more evident.

What is an advantage of using a stem-and-leaf plot of a histogram?

Stem-and_leaf plots contain original data values where histograms do not

Which statistic is the best unbiased estimator for μ?

The best unbiased estimated for μ is (1) x-bar

If a z-score is zero, which of the following must be true? Explin your reasoning. -The mean is zero -The corresponding is x-value is zero -The corresponding x-value is equal to the mean

The corresponding x-value is equal to the mean, because the z-score is equal to the difference between the x-value and the mean, divided by the standard deviation.

Explain how the interquartile range of a data set can be used to identify outliers.

The interquartile range (IQR) of a data set can be used to identify outliers because data values that are (1) greater than (2) Q3 + 1.5 (IQR) or (3) less than (4) Q1 - 1.5(IQR) are considered outliers

What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

The mean and standard deviation have the same values of μ=0 and σ=1

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. -A sampling distribution is normal only if the population is normal

The statement is false. A sampling distribution is normal if either n ≥ 30 or the population is normal

A students score on an actual exam is in the 78th percentile. What can you conclude about the student's exam score?

The student scored higher than 78% of the students who tool the actuarial exam

Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences. Compare the two curves.

The two curves will have (1) SAME LINE of symmetry. The curve with the larger standard deviation will be (2) MORE spread out than the curve with the smaller standard deviation.

Determine whether the variable is qualitative. Explain your reasoning. "Weights of fish caught during a derby"

The variable is (1) quantitative because weights are (2) numerical measurements

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. - As the size of a sample increases, the standard deviation of the distribution of sample means increases.

This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of a sample means decreases."

In a poll, 1,003 men in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos. "among the respondents, 47% said that they were in favor. Identify the population and the sample.

What is the population in the given problem? -all men in the country Identify the sample for the given problem -the 1,003 men selected

Given a data set, how do you know whether to calculate 'σ' or s?

When given a data set, one would have to determine if it represented the population of if it was a sample taken from the population. If the data are a population, then 'σ' is calculated. If the data are a sample, then s is calculated.

When estimating a population mean, are you more likely to be correct when you use a point estimate or an interval estimate? Explain you reasoning.

You are more likely to be correct using an interval estimate because it is unlikely that a point estimate will exactly equal the population mean.

Describe hoe you can transform a nonstandard normal distribution to the standard normal distribution. To transform a nonstandard normal distribution to the standard normal distribution you must transform each data value x into a z-score. Which of the following formulas is used to convert an x value into a z-score?

z = (X - μ) / σ

What is the difference between a census and a sampling?

A census includes the entire population. A sampling includes only part of the population.

How is a sample related to a population?

A sample is a subset of a population

The two main branches of statistics are ....

descriptive statistics and inferential statistics