# Project #17687 - Statistics

Must get an A, must show all work.

1. Holding all other variables constant, describe the change (if any) that arises for confidence intervals of the population proportion if:
A. The value of alpha is lowered. (Explain thoroughly).
B. The value of the sample proportion is diminished. (Explain thoroughly).

2. For each set of conditions, describe the test (either two, right, or left-tailed) which would be required to complete the hypothesis testing procedure and find the critical z value(s). In each case assume that the normal distribution applies.
A. = 0.01; H1 is p < 0.25
B. = 0.05; H1 is 0.45
C. = 0.10; H1 is p > 0.85
D. = 0.01; H1 is < 0.56

3. A chemist performing a series of thermodynamic experiments in which the mean temperature of the produced reactions is measured to be 0 degrees Celsius, with a standard deviation of one degree, wants to, identify the probability of obtaining the following temperatures:
(Utilize the appropriate diagrams to demonstrate the probabilities).
A. P (-1.24 B. P (z> 1.99) =
C. P (1.36 D. P (z > -3.41) =
E. P (z < 0.22) =
F. P (-1.96
4. When a student conducts a right-tailed test, the test statistic is calculated as z = 2.347. Using the traditional method of hypothesis testing, would you reject or fail to reject the null hypothesis when = 0.10? Explain why.

5. Identify the critical values that correspond to the indicated areas:
A. z0.9747
B. z0.1047
C. z0.5675

6. The metropolitan power authority in a small southern city is concerned about the voltage measurements that they have obtained from a number of residential houses in close proximity to the area specific plant. They have been measuring electricity at levels which are uniformly distributed between 167 and 178 voltages, far above what is standard for the forms of wiring utilized during the construction of the homes. A diagram of that distribution is prepared by an engineer as a facet of an emergency report submitted to the local town council about the situation. The vertical axis has a height of 0.25, with the voltage range represented on the horizontal. Reproduce that graphic and utilize it as reference to calculate the likelihood of the occurrence of the following voltage levels:
A. Less than 177.5?
B. Greater than 169.5?
C. Between 172.7 and 177.9?
D. Between 169 and 176.2?

7. Given the conditions in a nation abroad that:
Womens heights are normally distributed, with a mean of 59 inches and a standard deviation of 2.4 inches,
Mens heights are normally distributed, with a mean of 70 inches and a standard deviation of 3.9 inches,
The heights of shower fixtures in newly constructed homes are hung at 76 inches,
A. What percentage of men are able to fit beneath the shower heads comfortably?
B. What percentage of women can fit beneath the fixtures with ease?
C. Are the heights of the shower heads adequate in the new homes?
D. What shower head height would allow 89% of women to fit comfortably beneath the fixtures?

8. An assembly line operating in a computer product plant in China does a quality inspection evaluation by sampling 1800 of the products that it generates. It is found that 19.7% of the car parts that are utilized are faulty.
Create a 95% confidence interval for the percentage of the defective parts that are produced by the company and interpret the interval.
If the confidence level were to be increased to 99%, what would happen to the critical value, the margin of error and the confidence interval?

9. Birth weights in an emergent economy are normally distributed with a mean of 2,899 grams and a standard deviation of 310 grams, a significant rise above previously reported levels. The World Health Organization is, however, concerned about a small province in the nation, where obesity and malnutrition exist as concurrent concerns, due to the concentration of high/lower income households in close proximity to each other. Advisement from an exploratory team of public health experts from abroad was requested by local doctors when abnormal birth weights below 1900 grams (light) or more than 4,300 grams (unusually heavy) were reported in rising percentages. What is the percentage of babies who are of standard birth weights between 1900 to 4,300 grams?

10. In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in the New York Times). Test the claim of a somewhat common belief that such cancers are affected by cell phone use. That is, test the claim that cell phone users develop cancer of the brain or nervous system at a rate that is different from the rate of 0.0340% for people who do not use cell phones. Utilize a significance level of 0.05 and utilize the traditional method of hypothesis testing. Based on the obtained results, should cell phone users be concerned about cancer of the brain or nervous system?

11. In studying the language skills of groups of children, a psycholinguistic researcher administered the Communicative Development Inventory (CDI) to 90 children that come from low-income households. Their sentence complexity scores had a sample mean of 6.82 and a standard deviation of 7.18.
A. Construct an 80% confidence interval for the mean sentence complexity score of all low-income children. Write a statement outlining the significance of the obtained interval.
B. Suppose that it is known that the true mean sentence complexity score of high-income children is 17.88. Based on the above confidence interval, is there evidence that the true mean for low-income children differs from that of high-income children? Explain as thoroughly as is feasible.

12. In studying the effects of marketing exposure on young children, a researcher wanted to examine the claim that children would say that they preferred the taste of food if they associated it with the McDonalds brand name, even if the meals consumed were not from that company. When presented with carrots that were packaged with either plain wrapping or with a package that contained references to McDonalds, 54% of the randomly sampled 61 children said they preferred the carrots wrapped in the McDonalds packaging.
A. Find a 95% confidence interval for the population proportion of children that prefer the carrots wrapped in McDonalds packaging. Provide a statement addressing the significance of the finding.
B. Based on this confidence interval, could it be asserted that the majority (> 50%) of children would prefer the McDonalds carrots? Explain.

13. Laughter is often called the best medicine since it is hypothesized that the action within the body can elevate oxygen concentrations in the blood by increasing the heart rate of the individual. In the International Journal of Obesity, researchers investigated the heart rates of a sample of ninety subjects as they watched film clips designed to evoke mirth. During the laughing period, the heart rate of each subject was measured in beats per minute (bpm). The mean rate that was obtained was 82.5 (bpm), with a standard deviation of 10 bpm.

It is well known that the population mean resting heart rate of adults is 71 bpm. Using a significance level of 0.05 and the traditional method of testing, is there sufficient evidence to indicate that the true mean heart rate during laughter exceeds the rate when resting?

14. In tests of a radiator component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures:
518 548 561 523 536 499 538 557 528 563
At the 0.05 significance, test the claim that the modification to the component statistically increases the time between failures. Assume the times are normally distributed. Use the traditional method of hypothesis testing and calculate the required sample standard deviation.

15. In a sample of seven cars, each car was tested for nitrogen oxide emissions (in grams per mile) and the following results were obtained: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, and 0.15 (based on data from the EPA). Assuming that this sample is representative of the cars in use, construct a 98% confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars. If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, can we safely conclude that this requirement is being met?

16. Delineate, in two brief sentences, the advantages of the traditional method of hypothesis testing versus the p-value method.
B. Develop and solve, utilizing both testing approaches, a relevant example. Explain which method provides a stronger basis from which a claim asserted by researchers might be evaluated.

 Subject Mathematics Due By (Pacific Time) 11/24/2013 09:00 am
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