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STAT 121 - Credit Quiz 29 - with verified
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For the theoretical sampling distribution of x) created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and σ = 4, For the sampling distribution of x) described, what is its shape? a) Slightly right skewed b) Approximately Normal c) Slightly left skewed d) Cannot be determined because the shape of the population is
unknown - ANSWERS -c) Slightly left skewed
For the theoretical sampling distribution of x) created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and σ = 4 What is the standard deviation of the sampling distribution of x- bar a) 4 b) 1
c) .4 - ANSWERS -b) 1
For the theoretical sampling distribution of x) created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and σ = 4 What is the mean of the sampling distribution of x-bar? a) approximately 22 b) exactly 22
c) less than 22 - ANSWERS -b) exactly 22
For the theoretical sampling distribution of x) created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and σ = 4
What is the shape of a single sample of size 16? - ANSWERS -
Left skewed For the theoretical sampling distribution of x) created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and σ = 4 What is the mean of a single sample of size 16? a) exactly 22 b) close to 22 c) less than 22
d) greater than 22 - ANSWERS -b) close to 22
- Yes, b/c comparing new method to standard method
- Yes, b/c "randomly assigns" students to two groups
- Yes, there 50 students in each treatment group
- Yes, b/c this is a valid experiment A correlation of r = 0 indicates that a. no relationship of any form exists between x and y. b. x does not cause changes in y. c. the total variation in x cannot be explained by y.
d. x and y are not linearly related. - ANSWERS -d. x and y are
not linearly related. What is a distribution of a random variable? (this is very important to understand!!!!) a. The range of the values of a variable as centered around the mean. b. The numerical values placed on a histogram at varying points about the mean. c. A list of possible values of a variable together with how often each value occurs.
d. The position of a variable within an observed data set. -
ANSWERS -c. A list of possible values of a variable together with
how often each value occurs. Three children are in a room, ages 3, 4, and 5. A fourth child enters aged 4. What can we say about the mean and standard deviation of the ages? a. The mean stays the same, but the standard deviation increases. b. The mean stays the same, but the standard deviation decreases. c. The mean and standard deviation stay the same.
d. Both the mean and standard deviation increase. - ANSWERS -
b. The mean stays the same, but the standard deviation decreases.
Prediction interval - ANSWERS -We are 95% confident that the
final exam score of a person who scored a 78 on Exam 3 will be in the interval (50, 98)
Confidence Interval - ANSWERS -We are 95% confident that the
mean final exam score of all students who scored a 78 on exam 3 will be in the interval (70, 80). The chi-square test statistic measures
B. Only approximately Normal if the sample size is large enough to apply the Central Limit Theorem; i.e., whenever np0 ≥ 10 and n(1 - p0) ≥ 10. C. t when σ is unknown and standard Normal when σ is known just like for means. D. Approximately standard Normal whenever n > 40. -
ANSWERS -B. Only approximately Normal if the sample size is
large enough to apply the Central Limit When we compare proportions for two populations using categorical data from two independent samples, the appropriate statistic(s) is(are): A. pˆ B. pˆ1 and pˆ C. pˆ1 - pˆ D. pˆ1 / pˆ E. p1 and p
F. p1 / p2 - ANSWERS -C. pˆ1 - pˆ
Suppose you want to estimate the proportion of voters who will vote for Mary Bills, a candidate for state senator. How many should you sample in order to estimate p with a margin of error of 0.02 (2%) and 90% confidence? A. 2401 B. 1692
C. 609
D. 133
E. 21 - ANSWERS -B 1692 (Hint: use p* = 0.5)
In order to test the hypotheses H0: p = 0.7 versus Ha: p > 0.7, what checks should be made A. SRS and n > 40. B. SRS and np0 = n(0.7) ≥ 10 and n(1 -p0) = n(0.3) ≥ 10. C. SRS and population Normally distributed. D. SRS and no outliers or strong skewness in the data. -
ANSWERS -B. SRS and np0 = n(0.7) ≥ 10 and n(1 -p0) = n(0.3)
What does a chi-square test statistic close to zero indicate? A. A strong association between the row and column variables. B. A big disagreement between the data and the null hypothesis. C. No association between the row and column variable. D. Large differences between the observed and expected values. -
ANSWERS -C. No association between the row and column
variable. Two types of football helmets were analyzed to determine which had the lowest rate of damage. Of the 37 suspension-type football helmets, 24 were damaged when subjected to an impact test. Of
D. 0.358 - ANSWERS -D. 0.
Two types of football helmets were analyzed to determine which had the lowest rate of damage. Of the 37 suspension-type football helmets, 24 were damaged when subjected to an impact test. Of the 44 padded football helmets, 5 were damaged when subjected to the same impact test. We want to determine if there is a significant difference in damage rate of the two types of helmets. What is the value of the test statistic using 0.107 as the value of the standard error of pˆ1 - pˆ2? (Hint: 0.107 is the value of the entire denominator.) A. 5. B. 4. C. 3. D. 2.
E. 0.535 - ANSWERS -A. 5.
Two types of football helmets were analyzed to determine which had the lowest rate of damage. Of the 37 suspension-type football helmets, 24 were damaged when subjected to an impact test. Of the 44 padded football helmets, 5 were damaged when subjected to the same impact test. We want to determine if there is a significant difference in damage rate of the two types of helmets. Using 3.13 as the value of the test statistic (which it is not), what is the P-value for a two-sided test of hypothesis? A. 0.
B. 0.
C. 0.
D. 0.0313 - ANSWERS -C 0.0018: [2(0.009)] for a two-sided test
Two types of football helmets were analyzed to determine which had the lowest rate of damage. Of the 37 suspension-type football helmets, 24 were damaged when subjected to an impact test. Of the 44 padded football helmets, 5 were damaged when subjected to the same impact test. We want to determine if there is a significant difference in damage rate of the two types of helmets. If the P-value for a two-sided test were .002 (not the right answer), what should we conclude at the 1% level of significance? A. Reject the null hypothesis and conclude that the proportion of damage is significantly different for the two types of helmets. B. Reject the null hypothesis and conclude that the proportion of damage is not significantly different for the two types of helmets. C. Fail to reject the null hypothesis and conclude that the proportion of damage is significantly different for the two types of helmets.
D. Fail to reject t - ANSWERS -A. Reject the null hypothesis and
conclude that the proportion of damage is significantly different for the two types of helmets. Two types of football helmets were analyzed to determine which had the lowest rate of damage. Of the 37 suspension-type football helmets, 24 were damaged when subjected to an impact test. Of the 44 padded football helmets, 5 were damaged when subjected
What are the mean and standard deviation for the sampling distribution of pˆ for random samples of size 200 selected from the population described in question 14? A. 0.20, 0. B. 0.20, 0. C. 0.20, 0. D. 0.22, 0. E. 0.22, 0.
F. 0.22, 0.414 - ANSWERS -D. 0.22, 0.
What is the shape of the sampling distribution of pˆ for samples of size 200 taken from the population described in question 14? A. Doesn't have a shape because the population data are categorical. B. Shape is right skewed because 78% are zeros and only 22% are ones. C. Shape is approximately Normal because np = 44 and n(1 - p) =
D. Shape cannot be determined without more information. -
ANSWERS -C. Shape is approximately Normal because np = 44
and n(1 - p) = 156. Suppose we are testing H0: p = 0.4 versus Ha: p > 0.4 and the test statistic from our random sample results are z = 1.03. What can we conclude at the 5% level of significance?
A. The population proportion is significantly greater than 0.4. B. We have insufficient evidence to conclude that the population proportion is significantly greater than 0.4. C. The population proportion is equal to 0.4. D. Not enough information is given to draw conclusions. -
ANSWERS -B. We have insufficient evidence to conclude that
the population proportion is significantly greater than 0. On the basis of the following residual plot, is inference in regression appropriate? A. Yes, because points are random in a shoebox shape. B. Yes, because there is an outlier. C. No, because the megaphone shape indicates more variability in the y's for larger x values. D. No, because the smile pattern indicates lack of linearity. -
ANSWERS -C. No, because the megaphone shape indicates
more variability in the y's for larger x values. Data was collected on suicides committed in 1990. We want to test whether there is a significant relationship between method of suicide and gender. What is the appropriate null hypothesis for this test? Firearms Poison Hanging Other Total Male 16,285 3,221 3,688 1,530 24,
The chi-square test output is as follows: Chi-Sq = 91.774 + 288.094 + 4.969 + 21.480 + 367.037 + 1152.19 + 19.874 + 85.907 = 2031. DF = ?, P-Value = 0. What can you conclude? A. That gender and method of suicide are independent. B. That method of suicide is unrelated to gender. C. That method of suicide is associated with gender. D. That the proportion of women who commit suicide with firearms is approximately equal to the proportion of men. -
ANSWERS -C. That method of suicide is associated with gender.
Firearms Poison Hanging Other Total Male 16,285 3,221 3,688 1,530 24, Female 2,600 2,203 756 623 6, Total 18,885 5,424 4,444 2,453 30, Chi-Sq = 91.774 + 288.094 + 4.969 + 21.480 + 367.037 + 1152.19 + 19.874 + 85.907 = 2031. DF = ?, P-Value = 0. Which cell had the highest contribution to the test statistic? A. The male firearms cell. B. The female firearms cell.
C. The males poison cell. D. The females poison cell.
E. The females other cell. - ANSWERS -D. The females poison
cell. Firearms Poison Hanging Other Total Male 16,285 3,221 3,688 1,530 24, Female 2,600 2,203 756 623 6, Total 18,885 5,424 4,444 2,453 30, Chi-Sq = 91.774 + 288.094 + 4.969 + 21.480 + 367.037 + 1152.19 + 19.874 + 85.907 = 2031. DF = ?, P-Value = 0. What are the appropriate degrees of freedom? A. 1 B. 2 C. 3 D. 4
E. 8 - ANSWERS -C 3 (df = (#r - 1) (#c - 1) )
Tar fumes containing polycyclic aromatic hydrocarbons (PAH) are released from coke ovens in which coal is fired into coke, and workers are exposed to high levels of PAH. Jongeneelen et al. (1990) made air sample measurements of PAH concentration for three consecutive morning shifts from filters in masks worn by
Predictor Coef Stdev t-ratio p Constant 0.0030 0.1729 0.02 0. totPAH 0.119669 0.006800 17.60 0. s = 0.7160 R-sq = 87.3% R-sq(adj) = 87.0%
What are the values of the test statistic - ANSWERS -E. 17.
and 0. Tar fumes containing polycyclic aromatic hydrocarbons (PAH) are released from coke ovens in which coal is fired into coke, and workers are exposed to high levels of PAH. Jongeneelen et al. (1990) made air sample measurements of PAH concentration for three consecutive morning shifts from filters in masks worn by each of 47 coke oven workers. Urine samples were used to determine the level of pyrene (one of the hydro-carbons obtained in the dry distillation of coal) for each worker. A regression analysis was performed to determine whether x = the total PAH (μg/m^3) from the three measurements could be used to predict y = the amount of pyrene (μg/m^3). The results are as follows. The regression equation is pyrene = 0.003 + 0.120 totPAH Predictor Coef Stdev t-ratio p Constant 0.0030 0.1729 0.02 0. totPAH 0.119669 0.006800 17.60 0. s = 0.7160 R-sq = 87.3% R-sq(adj) = 87.0%
What is the average increase in y = the a - ANSWERS -E 0.
(Hint: Question gives interpretation of slope.) Tar fumes containing polycyclic aromatic hydrocarbons (PAH) are released from coke ovens in which coal is fired into coke, and workers are exposed to high levels of PAH. Jongeneelen et al. (1990) made air sample measurements of PAH concentration for three consecutive morning shifts from filters in masks worn by each of 47 coke oven workers. Urine samples were used to determine the level of pyrene (one of the hydro-carbons obtained in the dry distillation of coal) for each worker. A regression analysis was performed to determine whether x = the total PAH (μg/m^3) from the three measurements could be used to predict y = the amount of pyrene (μg/m^3). The results are as follows. The regression equation is pyrene = 0.003 + 0.120 totPAH Predictor Coef Stdev t-ratio p Constant 0.0030 0.1729 0.02 0. totPAH 0.119669 0.006800 17.60 0. s = 0.7160 R-sq = 87.3% R-sq(adj) = 87.0%
What are the assumptions necessary for th - ANSWERS -B. The
y's at each x are Normally and independently distributed with equal variances. Tar fumes containing polycyclic aromatic hydrocarbons (PAH) are released from coke ovens in which coal is fired into coke, and workers are exposed to high levels of PAH. Jongeneelen et al. (1990) made air sample measurements of PAH concentration for
