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The operation manager at the light bulb factory wants to determine whether there is any difference in the average life expectancy of bulbs manufactured on two different types of machines. The process standard deviation of Machine 1 is 110 hours and of Machine II is 125 hours. A random sample of 25 light bulbs obtained from Machine 1 indicates a sample mean of 375 hours, and a similar sample of 25 from Machine II indicates a sample mean of 362 hours.
(a) Using the 0.05 level of significance, is there any evidence of a difference in the average life of bulbs produced by the two types of machines?
The confidence interval must be less than 5 percentage points i.e. the confidence interval should extend at most 2.5 percentage points above and below the sample proportion?
An investigator wants to estimate caffeine consumption in high school students. How many students would be required to ensure that 95% confidence interval estimate for the mean caffeine intake (measured in mg) is within 15 units of the true mean? ..
We want to show that a real number, chosen at random from the interval [0,1], can be approximated to within 1/(n²) by rational numbers of the form k/n.
Years to Complete a Graduate Program: The average number of years a person takes to complete a graduate degree program is 3. The standard deviation is 4 months. Assume the variable is normally distributed. If an individual enrolls in the program, ..
Find the probability of each value of X. Draw a histogram to display this distribution. (Because probabilities are long-run proportions, a histogram with the probabilities as the heights of the bars shows what the distribution of X would be in ver..
If we wanted to shorten the interval of the estimation of the true mean of Saturday sales to a width of $600 in total, what should the size of our sample be to achieve it?
We are interested in comparing the proportions of males and females who think earning a large salary is very important to them. I surveyed 200 of each gender and recorded their answers to the question as yes or no.
Researcher expects 12 point treatment effect and plans to use two-tailed hypothesis test with u α = .05. Calculate the power of test if researcher uses a sample of n = 16 individuals.
Given a sample size of 9,245, a sample mean of 38, a standard deviation of 8.15, and a confidence level of 97%, calculate the lower bound of the confidence interval.
Interpreting confidence interval for the P-value. Give an appropriated response. A weight loss center provided a loss for 72% of its participants.
What is the distinction between a one-sided and a two-sided hypothesis test in this problem?
Note down a research that requires a decision making with probabilities.
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