Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic. The heart will last and operate almost indefinitely once it is implanted in the patient's body, but the battery pack needsto be recharged about every four hours. A random sample of 50 battery packs is selected and subjected to a life test. The average life of these batteries is 4.05 hours. Assume that battery life is normally distributed withstandard deviation o= 0.2 hour. Is there evidence to support the claim that mean battery life exceeds 4 hours? Use a= 0.05.What is the test statistic for the test? Answer rounded-off to 2 decimal places

Given;population mean(μ)=4 hourpopulation standard deviation(σ)=0.2 hoursample size(n)=50sample…

Answered: 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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One test for Diabetes is called the A1C test. It measures the percentage of red blood cells that have sugar-coated hemoglobin attached to them (called the A1C score). Assume that the distribution of A1C scores is normally distributed with a mean of 5.0 and a standard deviation of 0.5 (the actual mean and standard deviation are slightly above these values and are gender dependent. I have rounded to make calculations easier). Determine the probability of observing an A1C score greater than 6.06 i.e P(X > 6.06). Enter your answer to 4 decimal places.
Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic. The heart will last and operate almost indefinitely once it is implanted in the patient's body, but the battery pack needs to be recharged about every four hours. A random sample of 50 battery packs is selected and subjected to a life test. The average life of these batteries is 4.05 hours. Assume that battery life is normally distributed with standard deviation o= 0.2 hour. Is there evidence to support the claim that mean battery life exceeds 4 hours? Use a= 0.05. What is the P-value for the test? Answer with 6 decimal places
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 69 companies reported in The Wall Street Journal found a sample mean tenure of 8.8 years for CEOs with a standard deviation of s=s= 4 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 α=0.10α=0.10. Your hypotheses are: Ho:μ=9Ho:μ=9 Ha:μ<9Ha:μ<9What 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.) The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to...…
The gasoline consumption projected for a car model is 13 km / l. After the launch of the vehicle, a specialized magazine carried out a test that showed 1300 cars, an average consumption of 12.3 km / l. The manufacturer claims that the standard deviation of consumption is 0.5 km / l. test the hypothesis that consumption is at least 13km / l.
A group consists of 5 Democrats and 8 Republicans. 7 people are selected to attend a conference.a. In how many ways can 7 people be selected from this group of 13?b. In how many ways can 7 Republicans be selected from the 8 Republicans?c. Find the probability that the selected group will consist of all Republicans.
A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is lessthan 38,500 miles. To check the claim, the firm randomly selects and tests 28 of these tires and gets a mean lifetime of 37,550 miles with a standard deviation of 1250 miles. At α = 0.02, test the shipping firm's claim. Round the test statistic to the nearest thousandth.
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.
Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic. The heart will last and operate almost indefinitely once it is implanted in the patient's body, but the battery pack needs to be recharged about every four hours. A random sample of 50 battery packs is selected and subjected to a life test. The average life of these batteries is 4.05 hours. Assume that battery life is normally distributed with standard deviation o= 0.2 hour. Is there evidence to support the claim that mean battery life exceeds 4 hours? Use a= 0.05. What is the test statistic for the test? Answer rounded-off to 2 decimal places
The lifetime of a particular component is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. What is the 30th percentile of component lifetimes?
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 749 hours. A random sample of 28 light bulbs has a mean life of 726 hours. Assume the population is normally distributed and the population standard deviation is 57 hours. At a = 0.02, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e). A. C. Fail to reject Ho - Fail to reject Ho Fail to reject Ho- Reject Ho- Reject Ho Reject H, Reject Ho- 4 (c) Identify the standardized test statistic. Use technology. (Round to two decimal places as needed.)
The mean life of a certain type of motor is 10 years with a standard deviation of 2 years.Assume that the useful life of an engine follows a normal distribution. The manufacturerreplaces all motors that fail free of charge while under warranty. If the company is willing toreplace only 3% of the motors that fail, how long should a warranty be?
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):

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