Question 1

For the following question(s): A researcher is interested in whether the color of an animal's surroundings affects learning rate. She tests 16 rats in a box with colorful wallpaper. Assume that it is known that the average rat can learn to run this particular maze (in a box without any special coloring)in 25 trials, with a variance of 64; the distribution is normal. The mean number of trials to learn the maze for the group with the colorful wallpaper is 11.
-What is the standard deviation of the distribution of means?

Accepted Answer

The standard deviation of the distribution of means can be calculated using the formula: standard deviation = square root of (variance/sample size). In this case, the variance is known to be 64 and the sample size is 16. Therefore, the standard deviation of the distribution of means is the square root of (64/16), which is 2.00. Choice B is the correct answer.

Question 2

How do you find the Z score for a sample's mean on the distribution of means?

Accepted Answer

To find the Z score for a sample's mean on the distribution of means, we need to use the standard formula for changing a raw score to a Z score, using the mean and standard deviation of the distribution of means. The mean of the distribution of means is the same as the population mean, and the standard deviation of the distribution of means (also known as the standard error) is equal to the population standard deviation divided by the square root of the sample size. Using this information, we can calculate the Z score for a sample's mean on the distribution of means.

Question 3

The ____________ is the hypothesis-testing procedure used when there is more than one individual in the study's sample and the population variance is known.

Accepted Answer

The Z test is used when the sample size is larger than 30 and the population variance is known. It is used to test hypotheses about population means. Option B) F test is used for testing hypotheses about variances of two populations. Option C) T test is used when the population variance is unknown or very small sample sizes. Option D) K test is not a commonly used hypothesis-testing procedure.

Question 4

All of the following types of distributions are important for hypothesis testing EXCEPT:

Accepted Answer

The distribution of R scores is not a standard distribution used in hypothesis testing. Hypothesis testing typically involves the distribution of a population, the distribution of a sample taken from that population, and the distribution of means (sampling distribution).

Question 5

The difference between creating a Z score from a single score and creating one from a sample mean is that:

Accepted Answer

When creating a Z score from a sample mean, you use the mean and standard deviation from the distribution of means (also known as the standard error of the mean) rather than the individual data points' standard deviation. This accounts for the variability between sample means.

Question 6

For the following question(s): A researcher interested in relationships developed a questionnaire that measures the degree of affection adult men feel for their fathers. She has found that for the general population the distribution is skewed to the right, the mean degree of affection is 60, and the standard deviation is 16. The researcher now is wondering if men who themselves have just become new fathers will score higher on the scale than men in general. She samples a group of 100 new fathers and finds that their mean is 64.5.
26 What is the research hypothesis?

Accepted Answer

The answer of For the following question(s): A researcher interested...

Question 7

For a 99% confidence interval, you use the Z scores for the middle 99% of the normal curve, which comes out to:

Accepted Answer

The Z scores for the middle 99% of the normal curve are +2.58 and -2.58. This is a common rule for confidence intervals and can be found on a standard normal distribution table.

Question 8

For the following question(s): A researcher is interested in whether the color of an animal's surroundings affects learning rate. She tests 16 rats in a box with colorful wallpaper. Assume that it is known that the average rat can learn to run this particular maze (in a box without any special coloring)in 25 trials, with a variance of 64; the distribution is normal. The mean number of trials to learn the maze for the group with the colorful wallpaper is 11.
-What is the shape of the distribution of means?

Accepted Answer

The problem states that the distribution of the rats' learning rates is normal with a mean of 25 and variance of 64. The researcher is only testing a sample of 16 rats, so the distribution of means will also be approximately normal by the Central Limit Theorem.

Question 9

Why will you rarely see a Z test in a research article?

Accepted Answer

Z tests require knowledge of the population mean and standard deviation, and such information is rarely available in behavioral and social science research. Therefore, researchers often use t-tests, which only require knowledge of the sample mean and standard deviation.

Question 10

For the following question(s): A researcher interested in relationships developed a questionnaire that measures the degree of affection adult men feel for their fathers. She has found that for the general population the distribution is skewed to the right, the mean degree of affection is 60, and the standard deviation is 16. The researcher now is wondering if men who themselves have just become new fathers will score higher on the scale than men in general. She samples a group of 100 new fathers and finds that their mean is 64.5.
26 What is the research hypothesis?

Accepted Answer

The research hypothesis is that the population of new fathers has a higher mean than the mean of the population of men in general. The mean of the comparison distribution is the mean of the general population, which is 60.

Question 11

A region of scores estimated to include a population parameter such as the population mean is called:

Accepted Answer

A region of scores estimated to include a population parameter such as the population mean is called an interval estimate. A confidence interval is a specific type of interval estimate that also includes a level of confidence or probability. Therefore, both options B and C are correct. A point estimate is a single value estimate of a population parameter, such as the sample mean being used to estimate the population mean, but it does not provide a range or interval.

Question 12

A 99% confidence interval is the region:

Accepted Answer

A 99% confidence interval is constructed in such a way that there is a 99% chance that it includes the true population mean. This means that if we repeatedly take samples and construct confidence intervals in the same way, about 99% of the intervals will contain the true population mean. Option B is incorrect because it implies that 1% confidence is more credible than 99% confidence. Option C and D are both incorrect as they describe the proportion of scores included, rather than the likelihood that the interval contains the true population mean.

Question 13

The best estimate of the population mean is the:

Accepted Answer

The best estimate of the population mean can be obtained by calculating the sample mean. This is because the sample mean is an unbiased estimator of the population mean and provides a good estimate of the central tendency of the population. It takes into account all the values in the sample and is less affected by outliers compared to other measures of central tendency like the median or mode.

Question 14

For the following question(s): A researcher is interested in whether the color of an animal's surroundings affects learning rate. She tests 16 rats in a box with colorful wallpaper. Assume that it is known that the average rat can learn to run this particular maze (in a box without any special coloring)in 25 trials, with a variance of 64; the distribution is normal. The mean number of trials to learn the maze for the group with the colorful wallpaper is 11.
-What is the null hypothesis?

Accepted Answer

The null hypothesis typically states that there is no effect or no difference. In this case, it would be that the rate of learning for the population of rats tested with colorful wallpaper is no different than the population of rats tested under ordinary circumstances.

Question 15

The 95% confidence interval:

Accepted Answer

A 95% confidence interval will be narrower than a 99% confidence interval because it requires less certainty in the estimation of the population parameter, thus allowing for a smaller margin of error.

Question 16

For the following question(s): A researcher interested in relationships developed a questionnaire that measures the degree of affection adult men feel for their fathers. She has found that for the general population the distribution is skewed to the right, the mean degree of affection is 60, and the standard deviation is 16. The researcher now is wondering if men who themselves have just become new fathers will score higher on the scale than men in general. She samples a group of 100 new fathers and finds that their mean is 64.5.
26 What is the research hypothesis?

Accepted Answer

The answer of For the following question(s): A researcher interested...

Question 17

For the following question(s): A researcher interested in relationships developed a questionnaire that measures the degree of affection adult men feel for their fathers. She has found that for the general population the distribution is skewed to the right, the mean degree of affection is 60, and the standard deviation is 16. The researcher now is wondering if men who themselves have just become new fathers will score higher on the scale than men in general. She samples a group of 100 new fathers and finds that their mean is 64.5.
26 What is the research hypothesis?

Accepted Answer

Since the population of men in general is said to be skewed to the right, it's safe to assume that the comparison distribution will also be approximately normal due to the sample size being large (Central Limit Theorem).

Question 18

The shape of the distribution of means is approximately normal if either (a)each sample consists of 20 or more individuals or (b)the distributions of the populations of individuals is skewed to the left. (True or False)

Accepted Answer

The shape of the distribution of means will be approximately normal due to the Central Limit Theorem, which applies when the sample size is large (usually n ≥ 30) regardless of the population distribution shape, or if the population itself is normally distributed, regardless of sample size. The specific conditions mentioned (a 20 individual sample size or a left-skewed population distribution) do not guarantee a normal distribution of means.

Question 19

Suppose the sample mean's score on the comparison distribution is more extreme than the cutoff. What would the researcher conclude regarding the colorful wallpaper?

Accepted Answer

If the sample mean's score on the comparison distribution is more extreme than the cutoff, it means that the results are statistically significant and the null hypothesis can be rejected. In this case, the researcher would conclude that the color of the chamber had a significant effect on the rate of learning. Therefore, the correct answer is choice C.

Question 20

The Z score of the sample mean on the distribution of means is:

Accepted Answer

The Z score of the sample mean is conceptually similar to creating a Z score from a raw score because both involve standardizing a score by subtracting the mean and dividing by the standard deviation. However, in the case of the Z score of the sample mean, we use the estimated standard deviation of the sampling distribution instead of the population standard deviation. Therefore, choices A, B, and D are incorrect.

Quiz 6: Hypothesis Tests With Means of Samples