Question 1

Which of these is NOT an appropriate tool for locating a specific point on a normal bell-shaped curve?

Accepted Answer

Sum of squares is a measure of variability, not a tool for locating a specific point on a normal bell-shaped curve. Raw scores, z scores, and percentile rankings are all appropriate tools for this purpose.

Question 2

The average do-it-yourself bedroom makeover costs $475 with a standard deviation of $86 (fictional data).Tanya redoes her daughter's room for $654.What percent of bedroom makeovers cost less than Tanya spent? (Round z score to two decimal places.)

Accepted Answer

To find the percentage of bedroom makeovers that cost less than what Tanya spent, we first calculate the z-score using the formula: $z = \frac{X - \mu}{\sigma}$, where $X$ is Tanya's spending ($654), $\mu$ is the average spending ($475), and $\sigma$ is the standard deviation ($86). Plugging in the values, we get $z = \frac{654 - 475}{86} = \frac{179}{86} = 2.08$. Looking up a z-score of 2.08 in a standard normal distribution table or using a calculator, we find that approximately 98.12% of bedroom makeovers cost less than what Tanya spent.

Question 3

A one-tailed test effectively doubles the p level in that one tail.

Accepted Answer

This is true because in a one-tailed test, all of the p-value is allocated to one tail (either the upper or lower tail), whereas in a two-tailed test, the p-value is split between both tails. Therefore, the p-value in a one-tailed test can be thought of as double the p-value in a two-tailed test for that one specific tail.

Question 4

Replication can help determine the circumstances in which a finding holds true or not.

Accepted Answer

Replication involves repeating a study or experiment in order to confirm or contradict the original findings. By doing so, researchers can identify the circumstances in which a finding holds true and to what extent. This helps to establish the reliability and validity of the original findings, and to identify any potential limitations or factors that may impact the generalizability of the results.

Question 5

Replication is not warranted when a finding is new or unexpected.

Accepted Answer

Replication is actually especially important when a finding is new or unexpected, as it helps establish the validity and reliability of the initial finding.

Question 6

The crowdsourcing movement in research has led to open science.

Accepted Answer

Crowdsourcing in research allows for collaboration and sharing of data and ideas, which promotes open science practices.

Question 7

A _____ test makes assumptions about the population, whereas a _____test does not.

Accepted Answer

A parametric test makes assumptions about the population parameters, such as the mean or the standard deviation, whereas a nonparametric test does not rely on such assumptions and can be used with data that doesn't fit normal distribution or when the population parameters are unknown.

Question 8

Philip is going to proceed with data analysis on a sample of scores that violate many assumptions about the population of interest.Which test would be more appropriate to use?

Accepted Answer

If the sample violates assumptions about the population, nonparametric tests are more appropriate. Nonparametric tests do not rely on assumptions about the distribution of the population or the sample, making them useful in situations where parametric assumptions are not met. Skewness and bias are not relevant for determining the appropriate test in this situation.

Question 9

India converts her raw score on a memory scale to a z score and finds that her score corresponds to a z score of -0.92.She knows her score is below the mean.What percent of people scored lower than India on the memory scale?

Accepted Answer

A z-score of -0.92 indicates that India's score is below the mean, and the percentage of people who scored lower than her can be found using a standard normal distribution table or a calculator. A z-score of -0.92 corresponds to approximately 17.88% of the population scoring lower than India.

Question 10

Stephanie wonders whether college textbooks change in price as students advance in their academic work.She finds some national data on college textbooks that indicates the average price of a text is $96 with a standard deviation of $31.She decides to collect the prices of 30 textbooks that are required for senior-level courses at her university.She finds the average cost to be $89.What is the percentile rank of Stephanie's collection of books? (Round z score to two decimal places.)

Accepted Answer

The z-score is calculated as (89 - 96) / (31/√30) = -1.25. Using the z-table, a z-score of -1.25 corresponds to a percentile rank of approximately 10.75.

Question 11

A z test result of -1.94 would allow one to reject the null hypothesis, assuming a two-tailed test with p = 0.05.

Accepted Answer

A z test result of -1.94 does not exceed the critical value of approximately ±1.96 needed to reject the null hypothesis in a two-tailed test with a significance level of p = 0.05.

Question 12

Replication involves conducting the same study with the same people multiple times.

Accepted Answer

Replication involves conducting the same study with different people or a different sample to see if the results are consistent and can be generalized to a larger population.

Question 13

A nondirectional test looks in both tails of the distribution.

Accepted Answer

A nondirectional test examines both tails of a distribution, whereas a directional test only examines one tail.

Question 14

A z test result of 1.98 would allow one to reject the null hypothesis, assuming a two-tailed test with p = 0.05.

Accepted Answer

A z score of 1.98 corresponds to a p-value of approximately 0.05. Since the p-value is smaller than the significance level of 0.05, we can reject the null hypothesis. Therefore, the statement is true.

Question 15

Why is it important to check for violations of assumptions when hypothesis testing?

Accepted Answer

Checking for violations of assumptions is important because we are making inferences about the population of interest that will be maximally valid if specific requirements are met. Violations of assumptions can lead to biased or incorrect results, so it is essential to check for them and address them appropriately.

Question 16

A nondirectional test looks in neither tail of the distribution.

Accepted Answer

A nondirectional test (or two-tailed test) looks for effects in both tails of the distribution, not in neither. It tests for the possibility of an effect in either direction.

Question 17

A test is said to be _____ when it produces fairly accurate results even when the data suggest that the population might not meet some of the assumptions.

Accepted Answer

A test is said to be robust when it produces fairly accurate results even when the data suggest that the population might not meet some of the assumptions. In contrast, a parametric test assumes that the data follow a certain distribution, while a nonparametric test makes no such assumption. A nonlinear test refers to a test that involves a nonlinear relationship between variables, but this is not relevant to the question at hand.

Question 18

Replication involves conducting the same study with different people.

Accepted Answer

Replication involves conducting the same study with different people to test the reliability and validity of the original findings.

Question 19

A given distribution has a mean of 50 and a standard deviation of 5.When comparing a score of 55 to this distribution of scores, the percentile rank is _____, whereas comparing a mean of 55, based on a sample of 10, to a distribution of means created from this parent population will result in a percentile rank of _____.

Accepted Answer

The percentile rank of a score of 55 is 1.00, as it is one standard deviation above the mean. The percentile rank of a mean of 55, based on a sample of 10, is 3.16, as it is 1.6 standard deviations above the mean of the distribution of means.

Question 20

If a result is statistically significant, then chance is said to account for the outcome.

Accepted Answer

If a result is statistically significant, chance is unlikely to account for the outcome. Instead, it suggests that there is a real, meaningful difference or relationship occurring in the data.

Quiz 7: Hypothesis Testing With Z Tests