Psych 10

The sampling distribution of sample mean is

the distribution of sample means over repeated samples.

Researchers specify a Type I error rate α. The alpha level indicates

the probability of committing a Type I error only if the null hypothesis is true

Given a particular sample, we compute a 95% confidence interval for \mu μ as [112, 118]. Which of the following is NOT correct? If you find this question difficult, read again pp. 314-315 of our textbook.

the probability that \mu falls within [112, 118] is 0.95.

Two researchers select a sample for a population with a mean of 12.4 and a standard deviation of 9. Researcher A selects a sample of 30 participants. Researcher B selects a sample of 40 participants. Which sample is associated with a smaller standard error?

Researcher B's, because the sample size was larger.

Which of the following statements regarding the null hypothesis is true?

The null hypothesis always makes statements about the population, not sample.

A researcher directly controls for the probability of a ________, but does not directly control for the probability of a ________.

Type I error; Type II erro

Course grade (eg, A, B, C, D, F) is _______.

a discrete variable

The result of tossing a quarter coin is _____.

a discrete variable because the result can be either heads or tails

A doctor recorded the body temperature of all the 60 patients he saw this past week, and found the patients' average temperature is 100.2 degrees. If he is interested in the temperatures of these 60 patients only, this 100.2 degrees is ______. If he is interested in knowing the temperatures of all his patients over the last 3 months, the temperatures of these 60 patients can be considered ______.

a parameter; a sample

What decision(s) can a researcher make in hypothesis testing?

accept the alternative hypothesis retain the alternative hypothesis

In hypothesis testing, a researcher will never be able to _______

accept the null hypothesis

Suppose that a researcher uses random sampling and the sample size is decently large. If the shape of the distribution in this population is negatively skewed, then what is the shape of the sampling distribution of sample means?

approximately normally distributed

Given the regression equation \hat{Y}=5-2X Y 5 2 X , we know

C) if X increases by one unit, the predicted value will decrease by 2 points

A researcher selects a sample of 121 participants from a population with a mean of 32 and a standard deviation of 22. What is the standard error of the mean?

2.0

If the population standard deviation is 15 and we repeatedly draw samples of 25 observations each, the resulting sample means will have a standard error of

3

A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20. About 68% of the sample means in this sampling distribution

36 and 40

Given the regression equation \hat{Y}=5-2X Y 5 2 X , what is the predicted value of Y when X=3?

A) -1

If we want to understand how the average life expectancy for different countries varies as a function of the country's per capita alcohol consumption, we would most likely plot

A) life expectancy on Y-axis and alcohol consumption on X-axis

In the Formula One (F1) car racing game, drivers cannot be too tall or too short. Tall drivers are too big and heavy for the racing car, whereas short or light drivers are not physically strong enough. If we calculate the correlation coefficient between height and weight for F1 drivers, it should be ______ as compared to the correlation for people in general.

A) smaller in magnitude

Using the following possible choices, complete the four cells in the following table. Each choice can be used more than once, or not used at all. H0 is true H0 is false Reject H0 Cell (1) Cell (3) Fail to reject H0 Cell (2) Cell (4) Cell (1) = ____ Cell (2) = ___ Cell (3) = ___ Cell (4) = ___ The probability of Cell (1) happening is ____ The probability of Cell (2) happening is ____ The probability of Cell (3) happening is ___ The probability of Cell (4) happening is ___

CELL 1: Type I error CELL 2 :Correct decision CELL3:Correct decision CELL4:Type II error probs 1: alpha probs 2: 1-alpha probs3:1-beta probs4: beta

As sample size increases, the standard error of the mean

decreases

A histroy instructor tells his 8-th grade histroy class, that 45% of the students in the class got an A on the history final. This is an example of ________.

descriptive statistics

Human heart rate (beats per minute) is ________.

discrete because it must be whole numbers and cannot be divided into smaller parts can be treated as continuous in practice because it can take so many different values and the difference between any 2 adjacent values is small

Which of the following is NOT a step in hypothesis testing?

evaluate the plan

The results of a poll of some 500 people in Merced are used to estimate the opinion of all the residents in Merced. We are doing ________ statistics.

inferential

Indicate whether the following situation involves descriptive or inferential statistics: The sample data from a poll are used to estimate the opinion of the population.

inferential statistics

In hypothesis testing, a researcher's decision regarding the hypotheses

is based on a probability, can be incorrect sometimes, can be either to retain or to reject the null hypothesis

A researcher believes that increasing attention given to children will improve mean academic performance. In this case, the null hypothesis should be:

mean academic performance will decrease or remain the same

A researcher tries to demonstrate that increasing attention given to children will improve mean academic performance. In this case, the alternative hypothesis should be:

mean academic performance will increase

The average score for an entire population would be an example of a _______.

parameter

the correlation between two variables is a measure of the degree to which

points cluster together around some best-fitting straight line scores of one variable can be predicted from scores in the other variable ) one variable changes with the other variable

A researcher is curious about how well high school students in the US know about fairy shrimps. The knowledge of all the high school students in the US is an example of _______.

population

Although research questions usually concern a ______, the actual research is typically conducted with a _______.

population, sample

A researcher wants to know how well the rats in his lab are growing. He weighs each individual of the 25 lab rats in his lab, and calculates the average weight for them. The weights of these 25 rats form a ______. The average weight is an example of ________.

population; parameter

In hypothesis testing, a researcher can never

prove that his or her hypothesis is correct with 100% certainty

The covariance will always

reflects the direction of the relationship between two variables

In hypothesis testing, we set a Type I error rate α to minimize the probability of

rejecting a true null hypothesis

The first step to hypothesis testing requires that a researcher

state the hypotheses

A researcher wants to know the average weight of a certain type of rats. He weighs each individual of the 25 lab rats in his lab, and calculates the average weight for them. The average weight of the 25 rats is a _______.

statistic

The Student's t-distribution

will become more and more similar to the standard normal distribution as the degrees of freedom increase.

The average height of these 5 people is 58.6. If we have a new set of 5 different people, the average height of the new data ______.

will probably be different from 58.6, but not sure higher or lower

We are going to add extra data point to the following scatterplot. Which of the following candidate points, if added, will most seriously affect the correlation?

(A) (X=2, Y=4)

If the covariance between X and Y, covXY is 325, then what is the correlation between X and Y?

(A) must be positive

The Peason's correlation coefficient between two variables is defined as

(A) the covariance of those variables divided by the product of their standard deviations

Consider the following scatterplot. What would be a reasonable visual estimation of the correlation coefficient between the two variables?

(A) ─ 0.50

If for some variables X and Y, the correlation between X and Y is ─ 0.6, what is the correlation between Y and X?

(A) ─ 0.6, the same as the correlation between X and Y

Which of the following can best describe the patter in the above Q2 scatterplot?

(B) a straight line going from upper left to lower right

If higher scores of X tend to be paired with lower scores of Y, the covariance between X and Y will be

(B) negative

A researcher tries to study the correlation between salary and years of education. Instead of looking at people in general, he restricted his sample to those who dropped out from junior high school. In this study the correlation coefficient is only 0.20 and thus he concluded that education is only weakly related to salary. This conclusion could be best refuted by which of the following arguments?

(B) the sample is limited to junior high school drop-outs only, and thus the range where salary and education can vary are seriously limited. The correlation for people in general should be higher

For the regression equation \hat{Y}=5-2X Y 5 2 X , when X=0, what is the predicted value of Y?

(C) 5

Suppose the correlation coefficient between smoking and lung cancer is 0.75, then it means

(C) as smoking becomes heavier, lung cancer tends to happen more often

If we have a regression line predicting the amount of improvement in your performance as a function of the amount of private tutoring you receive, an intercept of 12 would mean that

(C) even without tutoring you will improve.

Consider the regression equation \hat{Y} = 5-2X Y 5 2 X . What can we learn from the negative slop b=-2 b 2 ? Hint: Sketch the regression line first before answering this question.

(C) the correlation between X and Y must be negative

For some variables X and Y, their correlation coefficient r is ─ 0.6. Then what is the covariance between X and Y, covXY ?

(C) we need standard deviations of X and Y to calculate that

Calculate the correlation coefficient r for this data set X Y 2 6 3 4 4 6 2 7 4 2

-0.625 (with margin: 0.02)

A researcher selects a sample of 64 participants from a population with a mean of 10 and a variance of 16. What is the standard error of the sample mean?

0.5

We know the central limit theorem says \bar{X} X approximately follows if n is large then which of the following is correct?

the variability of sample means \bar{X} is smaller than the variability of individual scores X. So extreme values of X can happen by chance, but extreme values of \bar{X} are much less likely to happen by chance. the sampling distribution of \bar{X} is approximately normal, regardless of the distribution of X in the population. So if the distribution of X is hard to study, we can try to change the problem to one about \bar{X}, whose distribution is easier to work with.the larger the sample size, the smaller the variability of \bar{X} is. So it is helpful to have more data.

If we have calculated a 90% confidence interval and we find that it does NOT include the population mean,

this can happen about 10% of the time in practice, because the 0.90 probability is about all the possible confidence intervals.

It makes a difference whether or not we know σ because

we need to employ t-distribution if the sample standard deviation is used.

With large sample size and a small population variance, the sample means usually

will be close to the population mean.