chapter 9

Which equation is the correct formula for the t statistic for a distribution of means? (X - μM)/s (μM - M)/σ (M - μM)/s (M -μM)/sM

(M -μM)/sM

To calculate df, subtract ____ from ____. 2; N 2; n 1; N 1; n

1; N

According to the Consumer Action group, the average credit card interest rate in 2010 was 12.83 percent (based on a sample of 39 cards). A researcher wanted to know if college students at her institution have different interest rates compared to this national statistic. If conducting a single-sample t test, which statement would serve as her research hypothesis? The national interest rate is higher than that of college students, on average. College students have different interest rates on average compared to the nation. The national interest rate is no different from that of college students. College students have the same interest rate as the nation.

College students have different interest rates on average compared to the nation.

single sample t test

Is a hypothesis test in which we compare data from one sample to a population for which we know the mean but not the standard deviation. Uses a distribution of means.

What is one benefit of increasing the sample size when using t distributions? Larger sample sizes cost less when running the experiment than small samples. Larger sample sizes reflect the parameters of the population more closely. Larger sample sizes make better graphs. Larger sample sizes distance themselves from z distributions.

Larger sample sizes reflect the parameters of the population more closely

Is it necessary to correct for error when calculating the standard error for a t test? Explain your answer. Yes; we are estimating the standard deviation of the population. Yes; we are estimating both the mean and standard deviation of the population. No; we already corrected the standard deviation and are now reflecting the size of the sample. No; we are estimating both the mean and standard deviation of the population.

No; we already corrected the standard deviation and are now reflecting the size of the sample.

An effect size of 0.53 was calculated on data after performing a hypothesis test with a single-sample t statistic in which the null hypothesis was rejected. What can be concluded about the results based on this information? The research hypothesis is supported, but the effect size is small. The sample data are significantly different from what was expected based on the population, with the sample mean 0.53 standard deviations greater than the population mean. The population mean is 0.53 standard error units greater than the sample mean, and the results are significant. The effect size is medium, which means there is a medium risk that a Type I error has occurred.

The sample data are significantly different from what was expected based on the population, with the sample mean 0.53 standard deviations greater than the population mean.

When there is uncertainty about the parameters of a population of interest, a t distribution is used instead of a z distribution. Is the t distribution wider or thinner than the z distribution and why? The t distribution is wider because we are less certain of the findings compared to the z distribution. The t distribution is thinner because we are less certain of the findings compared to the z distribution. They produce the same curve because they both use the population mean. They produce the same curve because they both use the standard deviation of the population.

The t distribution is wider because we are less certain of the findings compared to the z distribution.

Griffin is looking through a statistics text for a z table, but he can find only a t table in the index. What tip would best help him find the information he needs? Add 1 to all the scores in the t table to find the corresponding z statistic. Go to the library to look up the z table. Use a different distribution instead of a z distribution. Use the sample size of infinity listed in the t table because it is equal to the z table.

Use the sample size of infinity listed in the t table because it is equal to the z table.

Why does correcting the standard deviation to account for error in a t test make a much bigger difference for small samples than it does for larger ones? We subtract 1 from the sample size, which removes a greater proportion of the total and corrects to a greater degree for smaller sample sizes compared to larger ones. Small samples are biased. We add 1 to the sample size, which removes a greater proportion of the total for smaller sample sizes compared to larger ones. Large samples are biased.

We subtract 1 from the sample size, which removes a greater proportion of the total and corrects to a greater degree for smaller sample sizes compared to larger ones.

The t statistic is more _____ than the z statistic because one is less likely to observe an extreme t statistic. conservative liberal extreme representative

conservative

Critical t values _____ as the degrees of freedom _____. decrease; increase increase; increase decrease; decrease decrease; approach 0

decrease; increase

The symbol df stands for: distance from mean. degrees of freedom. distance from mode. degrees of f estimation.

degrees of freedom

t statistic

indicates the distance of a sample mean from a population mean in terms of the estimated standard error

"Degrees of freedom" refers to what on a t table for a single-sample t test? number of restrictions enforced on people in the sample total sample size of the distribution, N number of scores that are free to vary in estimating population parameters, N - 1 amount of variance in the t distribution

number of scores that are free to vary in estimating population parameters, N - 1

The _____ indicates the distance of a sample mean from a population mean in terms of the standard error. paired-sample t test z statistic t statistic standard deviation

t statistic

A researcher is comparing two groups. The population mean from which the samples come is known, but not the population standard deviation. Which test should be used? either the t or z test may be used neither the t or z test because more information is needed z test because the population parameters are known t test because standard deviation for the population must be estimated

t test because standard deviation for the population must be estimated

degrees of freedom

the number of scores that are free to vary when we estimate a population parameter from a sample n-1

In order to conduct a single-sample t test, one needs to know: the population mean and standard deviation and the standard error of the sample. all properties of the sample and the population. the mean of the sample and all properties of the population. the population mean and the properties of the sample.

the population mean and the properties of the sample.

Standard error is used in the calculation of both the z and t statistic, with the difference that: t statistics require fewer numeric calculations than z statistics. the standard error for the t statistic is estimated using the sample standard deviation. the z statistic is based on known properties of the sample being studied. the population standard deviation is the basis of standard error in the t test.

the standard error for the t statistic is estimated using the sample standard deviation.

A dot plot graphs all the data in a sample, with the range of scores along the _____ and a dot for each data point above the corresponding value. x-axis y-axis variance line of best fit

x-axis