##### In Norway, the distribution of birth weights for full-term infants whose gestational age is 40 weeks...

In Norway, the distribution of birth weights for full-term infants whose gestational age is 40 weeks is approximately normal with mean μ= 3500 grams. We wish to determine if the birth weights of full-term babies whose mothers smoked throughout pregnancy is less than those of non-smoking 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...

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...

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... 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 t-test? 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 t-test 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...

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​ t-distribution 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

##### Draw the feature space plot (scatter plot) for the Green-Red, NIR-Green and NIR-Red band combinations. Based...

1. Draw the feature space plot (scatter plot) for the Green-Red, NIR-Green and NIR-Red band combinations. Based on these plots, which two bands are the most correlated?
 105 97 85 82 82 81 108 104 93 82 81 81 106 109 102 88 81 81 106 108 103 89 84 81 105 106 104 95 89 83 104 102 98 94 90 86

Green

 128 115 95 89 89 90 129 124 109 94 89 89 128 133 125 102 93 89 129 134 124 101 95 90 130 128 126 112 104 92 128 125 118 108 104 96

Red

 102 97 91 91 91 92 104 101 96 92 90 90 103 106 100 92 90 89 102 106 101 93 92 89 102 103 102 97 95 90 101 99 98 99 98 94

NIR

In: Statistics and Probability

##### These are a few short answer questions I am stumped on. 1. What is the sampling...

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 t-test without it?

2. What are the assumptions of a two-sample t-test?

3. Why do we “pool” variance for a two-sample t-test? 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 α-level, 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...

 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...

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...

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?...

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...

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....

According to Readers Digest, 49% of primary care doctors think their patients receive unnecessary medical care. Use z-table.

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:...

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 full-precision 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...

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