In Norway, the distribution of birth weights for fullterm infants whose gestational age is 40 weeks is approximately normal with mean μ= 3500 grams. We wish to determine if the birth weights of fullterm babies whose mothers smoked throughout pregnancy is less than those of nonsmoking mothers. A sample of 17 babies born to mothers who smoked is collected. The sample mean is 3297 grams and the sample standard deviation is 430 grams.
Test your hypothesis at the α = 0.05 level and explain what the results mean.
In: Statistics and Probability
The Transportation Safety Authority (TSA) has developed a new test to detect large amounts of liquid in luggage bags. Based on many test runs, the TSA determines that if a bag does contain large amounts of liquid, there is a probability of 0.9 the test will detect it. If a bag does not contain large amounts of liquid, there is a 0.09 probability the test will conclude that it does (a false positive). Suppose that in reality only 1 in 100 bags actually contain large amounts of liquid.
a. What is the probability a randomly selected bag will have a positive test? Give your answer to four decimal places.
b. Given a randomly selected bag has a positive test, what is the probability it actually contains a large amount of liquid? Give your answer to four decimal places.
c. Given a randomly selected bag has a positive test, what is the probability it does not contain a large amount of liquid? Give your answer to four decimal places.
In: Statistics and Probability
A survey of several 11 to 13 year olds recorded the following amounts spent on a trip to the mall:
$28.43,$25.23,$23.98,$24.79,$29.05
Construct the 95% confidence interval for the average amount spent by 11 to 13 year olds on a trip to the mall. Assume the population is approximately normal.
Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
In: Statistics and Probability
An insurance company has the business objective of reducing the amount of time it takes to approve applications for life insurance. The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage in which policy pages are generated and sent for delivery. The ability to deliver the policies to customers in a timely manner is critical to the profitability of the service. During a period of one month, a random sampling of 27 approved policies is selected, and the total processing time, in days, is collected. These data are stored in the table called Insurance.
73 19 16 64 28 28 31 90 60 56 31 56 31 56 22 18 45 48 17 17 17 91 92 63 50 51 69 16 17
A. In the past, the mean processing time was 45 days. At the 0.05 level of significance, is there evidence that the mean processing time has changed in 45 days?
B. What assumption about the population distribution is needed to conduct the ttest?
C. Construct a boxplot or a normal probability plot to evaluate the assumption made in (b).
D. Do you think that the assumption needed in order to conduct the ttest in(a) is valid? Explain.
Use Excel to solve part C
In: Statistics and Probability
In a random sample of six microwave ovens, the mean repair cost was $75.00 and the standard deviation was $11.00. Assume the population is normally distributed and use a tdistribution to construct a 99% confidence interval for the population mean μ. What is the margin of error of μ? Interpret the results.
In: Statistics and Probability
Green 
Red 
NIR 
In: Statistics and Probability
These are a few short answer questions I am stumped on.
1. What is the sampling distribution of the difference between means? Why can’t you conduct an independent samples ttest without it?
2. What are the assumptions of a twosample ttest?
3. Why do we “pool” variance for a twosample ttest? What are the assumptions that make this possible? How does it benefit us?
5. Why is a confidence interval not a probability statement?
9. What is an effect size? What happens to an effect size when sample size increases/decreases? Why?
10. What is power? How is it related to the αlevel, sample size, and effect size?
In: Statistics and Probability
x (Bins)  frequency 
0  0 
1  0 
2  0 
3  2 
4  5 
5  8 
6  13 
7  33 
8  42 
9  66 
10  77 
11  105 
12  103 
13  110 
14  105 
15  84 
16  70 
17  51 
18  40 
19  27 
20  27 
21  15 
22  5 
23  7 
24  2 
25  2 
26  1 
27  0 
28  0 
29  0 
30  0 
(7) On the Histogram worksheet, calculate all frequencies of the distribution using the table shown. (To three decimal places) The relative frequency of all values in the (X ≤ 7) range is ______.
(8) On the Histogram worksheet, calculate all frequencies of the distribution using the table shown. (To three decimal places) The relative frequency of all values in the (9 ≤ X ≤ 18) range is ______.
(9) On the Histogram worksheet, calculate all frequencies of the distribution using the table shown. (To three decimal places) The relative frequency of all values in the (X ≥ 15) range is ______.
(10) On the Histogram worksheet, calculate all frequencies of the distribution using the table shown. (To three decimal places) The relative frequency of all values in the (12 ≤ X < 20) range is ______.
In: Statistics and Probability
The income distribution in two cities is the following
City A 
City B 

10000 – 12000 
10000 
5000 – 7000 
4000 
12000  14000 
5000 
7000 – 9000 
6000 
14000  16000 
20000 
9000 – 11000 
8000 
16000 – 18000 
50000 
11000 – 13000 
14000 
18000  20000 
40000 
13000 – 15000 
16000 
20000 22000 
2000 
15000  17000 
2000 
Find the standard deviation and the coefficient of Variation for each company and comment on the results.
In: Statistics and Probability
In a recent survey of 150 students at a large community college, 86 students said they were “regular” coffee drinkers. It is known that 64% of all students at that community college are “regular” coffee drinkers. Use this information to compute necessary quantities, and fill in the blanks: The average distance between the values of the sample proportion (from all possible random samples of 150 students from this community college) of "regular" coffee drinkers and the population proportion 0.64 of "regular" coffee drinkers in this community college is approximately_________. We estimate that the values of the sample proportion (from all possible random samples of 150 students from this community college) of "regular" coffee drinkers vary from the population proportion of "regular" coffee drinkers in this community college of 0.64 by about _________ , on average.
In: Statistics and Probability
When would a Parole Officer want to know the mean differences between two or more groups? Describe a situation, including why and how it would be used.
In: Statistics and Probability
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 46 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.50 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) the distribution of weights is normal the distribution of weights is uniform σ is unknown n is large σ is known (c) Interpret your results in the context of this problem. 1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters. The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01. 99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters. The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.80 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) male firefighters
In: Statistics and Probability
According to Readers Digest, 49% of primary care doctors think their patients receive unnecessary medical care. Use ztable.
a. Suppose a sample of 290 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care.
E(p)=
O(p)=
b. What is the probability that the sample proportion will be within (plus/minus) 0.03 of the population proportion. Round your answer to four decimals.
c. what is the probability that the sample poportion will be within (plus/minus) 0.05 of the population proportion. Round your answer to four decimals.
In: Statistics and Probability
Consider the following sample data for the relationship between advertising budget and sales for Product A: Observation 1 2 3 4 5 6 7 8 9 10 Advertising ($) 40,000 50,000 50,000 60,000 70,000 70,000 80,000 80,000 90,000 100,000 Sales ($) 240,000 308,000 315,000 358,000 425,000 440,000 499,000 494,000 536,000 604,000 What is the predicted sales quantity for an advertising budget of $68,000? Please round your answer to the nearest integer. Note that the correct answer will be evaluated based on the fullprecision result you would obtain using Excel.
In: Statistics and Probability
Suppose we have annual income for a sample of men and women provided below. Either using Excel or conducting this by hand, test to see whether the average annual income of men and women are the same. Conduct this at the 0.05 level. Make sure to test (also at the 0.05 level) that variances are the same. Show all your work or provide Excel output with a written explanation.
Men 
Women 
99000 
47000 
32500 
46500 
14500 
47200 
78000 
46900 
22000 
47300 
15000 
47250 
92000 
46750 
11000 
47100 
37000 

67000 
In: Statistics and Probability