STAT201: Quiz 6

What z-score would be used to indicate the lowest 20% of the normal curve?

-.84

Refer to EOC 6.34 for a table of NHL height and weight data. Nashville Predators player P.K. Subban is 72.0 inches tall. What is his z-score for height? (Make sure to include 2 decimal places in your answer.)

-0.51

A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6. *What is the z-score for a student who gets a 22 on this test?*

-1.55

According to the U.S. Department of Education, 1,026,000 high school seniors (rounded to the nearest thousand) took the ACT test as part of the college admissions process. The mean composite score was 21.1 with a standard deviation of 4.8. The ACT composite score ranges from 1 to 36, with higher scores indicating greater achievement in high school. *What is the z-score for a mean of 19.6 from a sample of 50 students from this population?* Round your answer to two decimal places.

-2.21

Which z-score will have the largest area of the normal curve to the right of it?

-3.07

One of the core properties about the t-statistic is that its value can range between:

-∞ to ∞

Based upon what you gleaned in the previous questions, what is NHL player P.K. Subban's table value for height? (Report the figure exactly as you see it in the Standard Normal Curve table.)

.30503

Refer to the sample NHL player data in EOC 6.34 and your understanding of the Standard Normal Distribution. What is the probability of an NHL player being heavier than Dustin Byfuglien? (Note: Your final answer should go to the fourth decimal place.)

0.0001

The upper tail probability associated with F(7,5) = 10.46 is _____.

0.01

What proportion of the normal distribution is below a z-score of -1.69. Round your answer to four decimal places.

0.0455

What is the (right tail) probability associated with a t-score of 1.725 with df=20?

0.05

A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6. Using the z-score found for the question above, *what proportion of the population falls below a score of 22 on this test?* Round your answer to four decimal places.

0.0606

What proportion of the normal distribution is above a z-score of 1.34?

0.0901

A student learns that on his most recent exam in environmental science, the sample mean was 67.08 with a standard deviation of 16.81. He scored a 75. If we assume that this is a population, and is normally distributed, what proportion of students in the class scored worse than this student? Enter your answer to four decimal places.

0.6808

What proportion of the normal distribution is above a z-score of -0.72? Round your answer to four decimal places.

0.7642

A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6. *Using the z-score found for the question above, what proportion of the population falls below a score of 43 on this test?*

0.8159

Click the proportion of the normal curve that is below z = 1.78

0.9625

The standard deviation of a population of IQ scores is 16. What is the standard error of the distribution of the sample means for samples of size 100?

1.6

The mean of a population of IQ scores is 100. What is the mean of the distribution of the sample means for samples of size 100?

100

The standard deviation of a population of IQ scores is 16. What is the standard error of the distribution of sampling means for samples of size 64?

2.0

Professor Anthony calculated a chi-square statistic of 16.22 with df=8. What is the critical value of chi-square in order to test whether or not the outcome falls within the upper 1% of the distribution?

20.09

According to the U.S. Department of Education, 1,026,000 high school seniors (rounded to the nearest thousand) took the ACT test as part of the college admissions process. The mean composite score was 21.1 with a standard deviation of 4.8. The ACT composite score ranges from 1 to 36, with higher scores indicating greater achievement in high school. An admissions officer wants to find what percentage of samples of 50 students will have a mean ACT score less than 19.6. What numbers from the information above will the admissions officer need? (mark all that apply)

21.1 4.8

According to the U.S. Department of Education, 1,026,000 high school seniors (rounded to the nearest thousand) took the ACT test as part of the college admissions process. The mean composite score was 21.1 with a standard deviation of 4.8. The ACT composite score ranges from 1 to 36, with higher scores indicating greater achievement in high school. According to the central limit theorem, what are the mean and standard error of the distribution of sample means for a sample of 50 students?

21.1 and 0.68

The mean of a normally distributed population is 225. What is the mode?

225.0

The median of a normally distributed population is 28. What is the mean?

28

You are concerned with the amount of time that teens spend doing online gaming, and you measure a random sample of 32 high school students with a mean of 28.6 hours per week. In calculating t-statistics, how many degrees of freedom (df) do you have?

31.0

The critical value of X^2(df=25) cutting off the top 5% of the distribution is _______.

37.65

The critical value of F(5,4) that cuts off the upper 2.5% of the distribution's tail is _______.

9.36

In a normal distribution with a mean of 100 and a standard deviation of 16, what score below is within one standard deviation from the mean?

90

The z-score distribution ________ has a mean of ________ .

Always; 0

There is a different F-distribution for every _________

Combination of degrees of freedom

The z, t, and F calculations have something in common: the denominator of the test statistic ______________.

Contains a measure of sample variability

Using the F critical values table, match the following sets of values with their critical values of F.

F(2 2) Prob .01 = 99 F (5 2) prob 0.25 = 39.9 F(3 4) prob 0.05 = 6.59 F(5 6) prob .001 = 20.8

If one scours the Internet for long enough, one can collect the heights and weights of all of the players in the National Hockey League (... yes, we did!) If you did too, you would find that they have a mean height of 73.03 inches with a standard deviation of 2.03 inches. The mean weight would be 202.18 pounds with a standard deviation of 15.73 pounds. Here are some data for four of those NHL players in 2017-18:Player/Team HEIGHT WEIGHTDustin Byfuglien (Winnipeg Jets) 75 260Dylan Ferguson (Vegas Golden Knights) 74 190Tom Wilson (Washington Capitals) 76 218Sidney Crosby (Pittsburgh Penguins) 71 200 Below, match each of the four players with their respective z-scores for height.

Ferguson --> +0.48 Wilson --> +1.46 Crosby --> -1.00

Which of the following is not actually a family of distributions?

Standard normal distribution

Which of the following is a characteristic of skewed distributions such as chi-square and F?

The critical values cutting off the identical areas of the upper and lower tails have differing absolute values

A population has a μ = 1185 and σ = 157. What additional information is needed to determine the standard error of the mean?

The size of the samples the means summarize is needed.

When could a z-test be used in place of a t-test?

When n is 30 or greater

If one is using nominal or ordinal level data, which distribution should be used?

X^2

In the previous question (wherein Professor Anthony calculated a chi-square statistic of 16.22 with df=8), would his outcome fall within the upper 5% of the distribution?

Yes

Which of the following would be indicated by a negative value for F?

an error in calculations

The F-table lookup procedure involves using two known values for ________.

degrees of freedom

Match the df to the value of t that cuts off .05 in the upper tail of the t-distribution.

df 4 = 2.132 df 9 = 1.833 df 21 = 1.721 df 30 = 1.697

The value of chi-square can be negative.

false

The rationale for degrees of freedom is that one value in a set of values with a known result is not ________.

free to vary

The distribution below presents a population of IQ scores with a mean of 100. Click the score that is as far below the mean as 123 is above.

left, between 70 and 80

The distribution of sample means approaches a normal curve as __________ increases to infinity?

n

The chi-square and F-distributions are ________ skewed.

positively

The F-ratio is a ratio of

two variances

mean of population symbol

μ

mean of the distribution of sample means symbol

μ_{X bar}

standard deviation of a population symbol

σ

standard error of the mean symbol

σ_{X bar}

Which z-score will have the largest area of the normal curve to the left of it?

-0.39

Match the z-score with the correct entry from the Standard Normal Table.

-2.96 --> .0015 -2.11 --> .0174 -1.15 --> .1251 -0.62 --> .2676

Click the proportion of the normal curve that is below z = 1.12

0.8686

A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6. *What is the z-score for a student who gets a 43 on this test?*

0.9

For 25 degrees of freedom, the critical value of chi-square cutting off 5% of the upper tail is χ2 (25) = 37.65. The critical value of chi-square for the same degrees of freedom that cuts off 1% of the upper tail will be ____________.25 df .05 = 37.65. The critical value for .01 will be

A larger value.

We tend to see a narrower normal curve when values are clustered around the mean, such as the ages of students in a college versus the ages of people in a small city, which are more spread out. The narrower the curve, the __________ the standard deviation.

smaller

Standard scores share a common distribution with a common mean and ________.

standard deviation

The original paper describing the t-distribution was published under the pseudonym ________.

student

A study of the habits of those who admit texting while driving has a single group of 25 participants. The dependent variable is reaction time to detect a sound, with a sample mean of 635 ms with a standard deviation of 143 ms. This test has a population mean of 600 milliseconds. Which test would be most appropriate to find the probability of obtaining this sample mean?

t

Sort the following z-scores in terms of the size of the area between the mean and the z-score, from smallest to largest.

+0.21 -0.34 +0.75 -1.97

What z-score cuts off the lower .7673 of the normal distribution? (Refer to Fig 6.12 for the Standard Normal Table.)

+0.73