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If a 90% confidence interval for the mean is found to be (1.25,4.75) using a sample of n=100, find the 95% confidence interval for the mean. a. Is this interval narrower or wider? Why? b. In general, explain how the sample size and the confidence level affect the width of a confidence interval.
Explain why the sampling distribution of the sample proportion is assumed to be Normal. Show your steps and write down any assumptions you make.
A clinic advertises that overweight patients can lose 40 pounds on average in a month if they follow the clinic’s diet and exercise program. Assume that the standard deviation for the amount patients lose is 5 pounds. Officials from health ministry suspect that the clinic is using false advertisement and want to investigate the clinic’s claim. They randomly sample 70 patients and find the sample mean is 35 pounds. What can you infer from this finding?
f X is a normally distributed random variable with a mean of 45 and a standard deviation of 8, find the following probabilities: a. P(X ">"> 50). b. P(X < 32). c. P(37 < X < 48). d. P(X = 45).
Assume that random variable N has the Poisson distribution with parameter lambda =0.1. (a) Find the probability mass function of X= N+ 1: (b) Does X have a Poisson distribution? Justify your answer. (c) Find the probability mass function of Y = 2X. (d) Does Y have a Poisson distribution? Justify your an
If X has uniform distribution over [0,1], find the density function and distribution function of Y D 3X: Identify the distribution of Y
Assume that X has the exponential distribution with parameter : Is it possible to find a function G .x/ such that Y D G .X/ has uniform distribution over [0; 1]? Justify your answer!
Determine the given of the problems below and formulate the null and alternative hypotheses both in words and symbols.
1. A teacher conducted a study to know if blended learning affects the students performances. A class of 30 Grade 11 students was surveyed and found out that their mean score was 83 with a standard deviation of 4. A study from other country revealed that μ=80 with a standard deviation of 3. Test the hypothesis at 0.10 level of significance.
2. A mathematics teacher in senior high school developed a problem-solving test for randomly selected 40 grade 11 students. These students had a average score of 85 and a standard deviation of 5. If the population had a mean score of 90 and a standard deviation of 3, use 5% level of significance to test the hypothesis.
The number of people arriving at a post office in a small town follows a Poisson distribution. On average, five people arrive at the post office in one minute. Find the probability that in a given minute,
A) more than two people arrive at the post office
B) less than eleven people arrive at the post office
c) between six and ten people arrive at the post office
The number of people arriving at a post office in a small town follows a Poisson distribution. On average, five people arrive at the post office in one minute. Find the probability that in a given minute,
A) more than two people arrive at the post office
B) less than eleven people arrive at the post office
c) between six and ten people arrive at the post office
