5. Medical researchers have developed a newartificial heart constructed primarily of titaniumand plastic. The heart will last and operatealmost indefinitely once it is implanted in thepatient's body, but the battery pack needs to berecharged about every 4 hours. A randomsample of 50 battery packs is selected andsubjected to a life test. The average life of thesebatteries is 4.05 hours. Assume that battery lifeis normally distributed with standard deviation0=0.2 hour.5.1. Is there evidence to support the claim thatmean battery life exceeds 4 hours? Use a=0.05.5.2. What is the P-value for the test?5.3. Explain how the question could beanswered by constructing a one-sidedconfidence bound on the mean life.

Solution: 5. Let X be the battery life. From the given information, n=50, x-bar=4.05 hours and σ=0.2…

Answered: 5. Medical researchers have developed a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 9 years. A survey of 120 companies reported in The Wall Street Journal found a sample mean tenure of 7.3 years for CEOS with a standard deviation of s = 5.8 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed. You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of a = 0.001. Your hypotheses are: H.:µ 29 На : и <9 What is the test statistic for this sample? test statistic = * (Report answer accurate to 3 decimal places.) What is the p-value for this sample? p-value = * (Report answer accurate to 4 decimal places.)
A sample of 10 from population 1 has a mean of 32 and a standard deviation of 6. A sample of 13 from population 2 has a mean of 48 and a standard deviation of 8. The population standard deviations are unknown but assumed to be equal. Test the hypothesis, at the 1% level of significance, that the population means are the same. State your conclusion as a sentence and include the test statistic and the critical value.
The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. According to the Empirical Rule, about what percent of the products last between 0 and 3 days?
A study of working actors looked at age and gender. One sample of 50 male actors had a mean age of 26 and a standard deviation of 5. The other sample included 50 female actors with a mean age of 36 and a standard deviation of 3. Estimate with 93% confidence the difference between the average ages of working male (μ1μ1) and female (μ2μ2) actors. Round answers to the nearest hundredth.
Daily Driving The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than24 miles per day. She selects a random sample of 25 drivers over the age of 60 and finds that the mean number of miles driven is 23.4. The population standard deviation is 4.1 miles. At=α0.01, is there sufficient evidence that those drivers over 60 years old drive less than 24 miles per day on average? Assume that the variable is normally distributed. Use the critical value method with tables. State the hypotheses and identify the claim with the correct hypothesis. :H0 =μ24 ▼not claim :H1 <μ24 ▼claim the hypothesis test is a ▼one-tailed test. Part 2 of 5 Find the critical value(s). Round the answer to at least two decimal places. If there is more than one critical value, separate them with commas. Critical value(s):
A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 10 years. A survey of 84 companies reported in The Wall Street Journal found a sample mean tenure of 8 years for CEOS with a standard deviation of s = 5.6 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed. You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of a = 0.10. Your hypotheses are: Но: и > 10 Ha: µ < 10 What is the test statistic for this sample? test statistic = (Report answer accurate to 3 decimal places.) What is the p-value for this sample? p-value = (Report answer accurate to 4 decimal places.)
Bacteria in a culture live for an average time of three hours with a standard deviation of 15 minutes. If it wasn’t normally distributed, at least what fractionof the bacteria live between one and five hours?

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