The part diameters are normally distributed. The lower tolerance limit corresponds to -2 z (minus two standard deviations below the mean). The upper tolerance limit corresponds to 3 z. What percent of parts will be out of tolerance? Describe the method you used to find the answers.
In: Statistics and Probability
An article reported the following data on oxidation-induction time (min) for various commercial oils: 88 104 130 160 180 195 132 145 213 105 145 151 153 136 87 99 95 119 129 (a) Calculate the sample variance and standard deviation. (Round your answers to three decimal places.) s2 = min2 s = min (b) If the observations were reexpressed in hours, what would be the resulting values of the sample variance and sample standard deviation? Answer without actually performing the reexpression. (Round your answer to three decimal places.) s2 = hr2 s = hr
In: Statistics and Probability
A certain article reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks) when holes were drilled in a certain brass alloy. 12 14 20 23 32 37 40 43 48 51 58 61 64 66 69 70 75 77 78 79 81 83 86 90 91 93 96 100 102 105 106 106 113 119 124 135 138 141 147 157 162 169 184 206 247 264 289 323 389 512 Compute the sample median, 25% trimmed mean, 10% trimmed mean, and sample mean for the lifetime data. (Round your answers to two decimal places.) sample median 25% trimmed mean 10% trimmed mean sample mean
In: Statistics and Probability
A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 94%. If it is known that returns are normally distributed with a mean of 6.2%, what is the risk, measured by standard deviation, that this investment manager assumes in his calculation? (Round "z" value to 2 decimal places and final answer to 2 decimal places. Note: if you get 7.52 % for your answer, enter it as .08. 7.52% is .0752, so rounding it to 2 decimal places gives .08)
In: Statistics and Probability
There are quarters of sales data
500,350,250,400
450,350,200,300
350,200,150,400
550,350,250,550
550,400,350,600
750,500,400,650,850
Using Minitab 18.0 Winter's time series forecasting method forecast 3 quarters ahead
The weights are level=.2;trend=.2;seasonal=.2
In: Statistics and Probability
The May 1, 2009, issue of a certain publication reported the following home sale amounts for a sample of homes in Alameda, CA that were sold the previous month (1,000s of $). 589 814 580 606 354 1,290 405 535 554 681 (a) Calculate and interpret the sample mean and median. The sample mean is x = thousand dollars and the sample median is x tilde = thousand dollars. This means that the average sale price for a home in this sample was $ and that half the sales were for less than the Correct: Your answer is correct. price, while half were more than the Correct: Your answer is correct. price. (b) Suppose the 6th observation had been 985 rather than 1,290. How would the mean and median change? Changing that one value lowers the sample mean but has no effect on the sample median. Changing that one value has no effect on the sample mean but raises the sample median. Changing that one value has no effect on either the sample mean nor the sample median. Changing that one value raises the sample mean but has no effect on the sample median. Changing that one value has no effect on the sample mean but lowers the sample median. (c) Calculate a 20% trimmed mean by first trimming the two smallest and two largest observations. (Round your answer to the nearest hundred dollars.) $ (d) Calculate a 15% trimmed mean. (Round your answer to the nearest hundred dollars.) $
In: Statistics and Probability
In a survey of 3939 adults, 705 say they have seen a ghost. Construct a 99% confidence interval for the population proportion. Interpret the results.
A 99% confidence interval for the population proportion is ( , ). (Round to three decimal places as needed.) Interpret your results.
Choose the correct answer below.
A. With 99% confidence, it can be said that the sample proportion of adults who say they have seen a ghost is between the endpoints of the given confidence interval.
B. With 99% confidence, it can be said that the population proportion of adults who say they have seen a ghost is between the endpoints of the given confidence interval.
C. With 99% probability, the population proportion of adults who say they have not seen a ghost is between the endpoints of the given confidence interval.
D. The endpoints of the given confidence interval show that 99% of adults have seen a ghost.
In: Statistics and Probability
Each box of Healthy Crunch breakfast cereal contains a coupon entitling you to a free package of garden seeds. At the Healthy Crunch home office, they use the weight of incoming mail to determine how many of their employees are to be assigned to collecting coupons and mailing out seed packages on a given day. (Healthy Crunch has a policy of answering all its mail on the day it is received.) Let x = weight of incoming mail and y = number of employees required to process the mail in one working day. A random sample of 8 days gave the following data.
x (lb) | 14 | 22 | 15 | 6 | 12 | 18 | 23 | 25 |
y (Number of employees) | 7 | 10 | 9 | 5 | 8 | 14 | 13 | 16 |
In this setting we have Σx = 135, Σy = 82, Σx2 = 2563, Σy2 = 940, and Σxy = 1530.
(f) Find Se. (Round your answer to three
decimal places.)
Se =
(g) Find a 95% for the number of employees required to process mail
for 14 pounds of mail. (Round your answer to two decimal
places.)
lower limit | employees |
upper limit | employees |
(h) Test the claim that the slope β of the population
least-squares line is positive at the 1% level of significance.
(Round your test statistic to three decimal places.)
t =
Find or estimate the P-value of the test statistic.
P-value > 0.250
0.125 < P-value < 0.250
0.100 < P-value < 0.125
0.075 < P-value < 0.100
0.050 < P-value < 0.075
0.025 < P-value < 0.050
0.010 < P-value < 0.025
0.005 < P-value < 0.010
0.0005 < P-value < 0.005
P-value < 0.0005
Conclusion
Reject the null hypothesis, there is sufficient evidence that β > 0.
Reject the null hypothesis, there is insufficient evidence that β > 0.
Fail to reject the null hypothesis, there is sufficient evidence that β > 0.
Fail to reject the null hypothesis, there is insufficient evidence that β > 0.
(i) Find an 80% confidence interval for β and interpret
its meaning. (Round your answers to three decimal places.)
lower limit | |
upper limit |
Interpretation
For each less pound of mail, the number of employees needed increases by an amount that falls within the confidence interval.
For each additional pound of mail, the number of employees needed increases by an amount that falls outside the confidence interval.
For each additional pound of mail, the number of employees needed increases by an amount that falls within the confidence interval.
For each less pound of mail, the number of employees needed increases by an amount that falls outside the confidence interval.
In: Statistics and Probability
CASE STUDY: Chest Sizes of Scottish Militiamen (p. 306):
Chest Size |
Frequency |
33 |
3 |
34 |
19 |
35 |
81 |
36 |
189 |
37 |
409 |
38 |
753 |
39 |
1062 |
40 |
1082 |
41 |
935 |
42 |
646 |
43 |
313 |
44 |
168 |
45 |
50 |
46 |
18 |
47 |
3 |
48 |
1 |
In: Statistics and Probability
1. Test the claim that the proportion of people who own cats is
significantly different than 30% at the 0.2 significance
level.
The null and alternative hypothesis would be:
a) H0:μ≤0.3
Ha:μ>0.3
b) H0:p≥0.3
Ha:p<0.3
c) H0:μ≥0.3
Ha:μ<0.3
d) H0:p≤0.3
Ha:p>0.3
e) H0:μ=0.3
Ha:μ≠0.3
f) H0:p=0.3
Ha:p≠0.3
The test is:
-left-tailed
-two-tailed
-right-tailed
Based on a sample of 400 people, 31% owned cats
The p-value is: ____? (to 2 decimals)
Based on this we:
2. You wish to test the following claim (HaHa) at a significance
level of α=0.01α=0.01.
Ho:μ=89.7
Ha:μ≠89.7
You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=12 with
mean M=93.7 and a standard deviation of SD=8.6
What is the p-value for this sample? (Report answer accurate to
four decimal places.)
p-value = ______?
The p-value is...
This p-value leads to a decision to...
As such, the final conclusion is that...
In: Statistics and Probability
Suppose you have a bag of 100 coins. Ninety of them are fair coins, which is P(H) = P(T) = 1/2. The other 10 coins are biased , they have tail (T) on both sides. Let X = {X1, X2, · · · , X100} be a random variable denoting the the total number of heads in the 100 coin flips.
a. How many possible values X can take? For example, if one tosses two fair coins, the number of total heads could be 0, 1, 2.
b. How many ways the value of X could be 1?
c. How many ways the value of X could be 2?
d. How many ways the value of X could be 25?
In: Statistics and Probability
The Wind Mountain archaeological site is located in southwestern New Mexico. Wind Mountain was home to an ancient culture of prehistoric Native Americans called Anasazi. A random sample of excavations at Wind Mountain gave the following depths (in centimeters) from present-day surface grade to the location of significant archaeological artifacts†.
85 | 45 | 120 | 80 | 75 | 55 | 65 | 60 |
65 | 95 | 90 | 70 | 75 | 65 | 68 |
(b) Compute a 98% confidence interval for the mean depth μ at which archaeological artifacts from the Wind Mountain excavation site can be found. (Round your answers to one decimal place.)
lower limit | cm |
upper limit | cm |
In: Statistics and Probability
Describe examples of situations where you could appropriately use the following. Explain why the procedure is the correct one to use and identify the statistic to be used and explain why that is the correct choice. (1 point each)
Describe procedure for following and provide an example of the calculations:
In: Statistics and Probability
In: Statistics and Probability
A. As a health policy expert, you are interested in knowing whether men and women in the United States differ in the frequency they visit doctors when sick. So you conduct a survey of 134 people and ask them how often they visit a doctor when they are sick. The results from this sample are as follows:
Frequency visit doctor |
||||
Sex |
Always |
Sometimes |
Never |
Total |
Men |
13 |
41 |
27 |
81 |
Women |
24 |
19 |
10 |
53 |
Total |
37 |
60 |
37 |
134 |
Perform the appropriate hypothesis test, at alpha = .01, to determine whether there is a relationship between sex and the frequency with which individuals in the United States visit doctors. You must show your hand calculations for this problem. Describe your hypotheses, results, and conclusion in a brief paragraph. If it is appropriate, you should also discuss the strength of the relationship based upon a suitable measure.
B . Show in a table or explain in words what the crosstabulation for your two variables from
Question above would look like if there were absolutely no association between the independent variable and the dependent variable.
In: Statistics and Probability