Statistics Final Prep

What is the total area under the normal curve?

1

For the same sample statistics, which level of confidence would produce the widest confidence interval?

99% because as the level of confidence increases, zc increases.

What is the difference between a census and a sampling?

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

What is the difference between a polygon and an ogive?

A frequency polygon displays class frequencies while an ogive displays cumulative frequencies

What are the two main branches of statistics?

Descriptive and Inferential

T/F A placebo is an actual treatment

F: A placebo is a fake treatment

T/F A sampling distribution is normal only if the population is normal

F: A sampling distribution is normal if either n is greater than or equal to 30 or the population is normal

T/F A large P-Value in a test will favor a rejection of the null hypothesis

F: A small P-Value in a test will favor a rejection of the null hypothesis

T/F As the size of a sample increases, the mean of the distribution of sample means increase

F: As the size of a sample increases, the mean of the distribution of sample means does not change

T/F In a hypothesis test, you assume the alternative hypothesis is true?

F: In a hypothesis test, you assume the null hypothesis is true

T/F: A statistic is a measure that describes a population characteristic.

False: A statistic is a measure that describes a sample characteristics

What is a disadvantage of using a stem and leaf plot instead of a histogram?

Histograms easily organize data of all sizes where steam and leaf plots do not

Why should the number of classes in a frequency distribution be between 5 and 20?

If the number of classes in a frequency distribution is not between 5 and 20, it may be difficult to detect any patterns.

From a random sample of 46 business days, gold prices had a mean of $1365.43. Assume the population standard deviation is $203.50. This creates a 90% confidence interval for the population mean of ($1316.08, $1414.78) Does it seem possible that the population mean could equal the sample mean exactly?

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

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

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

In hypothesis testing, does choosing between the critical value method affect your conclusion?

No, because both involve comparing the test statistic's probability with the level of significance.

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

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

When P is greater than a, does the standardized test statistic lie inside or outside the rejection region?

Outside, when the standardized test statistic is inside the rejection region, p is less than a

The interquartile range (IQR) of a data set can be used to identify outliers because data values that are greater than ___________ or less than __________ are considered outliers.

Q3+1.5(IQR) Q1-1.5(IQR)

What is the difference between relative frequency and cumulative frequency?

Relative frequency of a class is the percentage of the data that falls in that class, while cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.

What is replication in an experiment and why is it important?

Replication is repetition of an experiment under the same or similar conditions. It is important because it enhances the validity of the results.

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

Stem and leaf plots contain original data values where histograms do not

In order to predict y-values using the equation of a regression line, what must be true about the correlation coefficient of the variables?

The correlation between variables must be significant

What does it mean to say "correlation does not imply causation"?

The fact that two variables are strongly correlated does not in itself imply a cause-and-effect relationship between the variables

A student's score on an actuarial 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 took the actuarial exam

What conditions are necessary in order to use a one-way ANOVA test?

There must be at least 3 samples. The samples must be independent of each other. Each population must have the same variance. The samples must be randomly selected from a normal, or approx normal, population.

T/F If you decide to reject the null hypothesis, then you an support the alternative hypothesis

True

Given the data set, how do you know whether to calculate o~ 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 o~ is calculated. If the data is a sample, then s is calculated

The two curves will have __________ of symmetry. The curve with the larger standard deviation will be ________ spread out than the curve with the smaller standard deviation.

the same line more

To transform a nonstandard normal distribution to the standard normal distribution you must transform each data value x into a z-score. What is the formula?

z=x-u / o~

What is the difference between an observational study and an experiment?

In an experiment, a treatment is applied to part of a population and responses are observed in an observational study, a researcher measures characteristics of interest of part of a population but does not change existing conditions.

Explain the difference between the z-test for u using rejection regions and the z-test for u using a P-Value

In the z-test using rejection regions, the test statistic is compared with critical values. The z-test using a p-value with the level of significance, a.

What are some benefits of using graphs of frequency distributions?

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

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

The mean and standard deviation have the values, u=0 and o~=1

What conditions are necessary in order to use a t-test to test the difference between two population means?

The population standard deviations are unknown. The samples are randomly selected and independent. The populations are normally distributed or each sample size is at least 30

What conditions are necessary in order to use the z-test to test the difference between two population means?

The samples must be independent Each population has a normal distribution with a known standard deviation The samples must be randomly selected

Explain the relationship between variance and standard deviation. Can either of theses measures be negative?

The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.