Brian is interested in how many bottles of beer typical Americans drink in a yea

Question

Brian is interested in how many bottles of beer typical Americans drink in a year Let denote a random variable indicating the number of bottles one person drinks a year Brian believes that the average Americans drink 100 bottles of beer in a year, so that the population mean of is equals to 100. But, he wants to test whether his hypothesis is correct by looking at a random sample Write down the hypotheses that Brian is going to test. To test the hypothesis, Brian selected a random sample of 9 CSULB students, and their responses on are as follows: 90, 80, 150, 110, 5, 180, 0, 220, 20 Compute the sample mean and the sample standard deviation of Compute the test statistic. Brian wants to limit the probability of making the Type I error at 5%. what is the critical value? Finally judge whether he would reject the null hypothesis or not. Answer by drawing an appropriate probability density curve The US Department of Health and Human Services is concerned about increasing obesities among the American adults. The department surveyed the whole US population 10 years ago. As a result, the average male weight was 190 (unit: pound) and the variance of the male weight was 285 In this year, due to the limitation of budget, the department has selected a random sample of 101 male adults. The sample mean of the male weight is 198 (pounds) The sample variance of the male weight is 368 While assuming no significant change in the average weight of Americans, the department is trying to judge from the sample whether the average American weight has increased over the past decade. Does the sample allow the department to conclude that the average American weight has increased? Determine whether the P-value (that would be obtained from the hypothesis testing in (a) is greater or smaller than 0.05. Explain the reason by drawing an appropriate probability density curve Carry out a hypothesis testing of whether the population variance in the current year has a different value from that of 10 years ago Carol is interested in overall level of house prices in California. In particular, he wants to estimate the confidence interval of population mean of house price (per square foot in dollar) For estimation, he selected a random sample of 1000 houses, and found that the sample mean of house price per square foot is 4.8 and the standard deviation of house price per square foot is 2 Estimate the 95% confidence interval of the population mean of house price (per square foot).

Explanation / Answer

Brain is going to use Null hypothesis
Mean of the sample data: ((90+80+150+110+5+180+0+220+20)/9)=95
Standard deviation:

for each number:
(90-95)^2=25
(80-95)^2=225
(150-95)^2=3052
(110-95)^2=225
(5-95)^2=8100
(180-95)^2=7225
(-95)^2=9025
(220-95)^2=15625
(20-95)^2=5625
So,square root of mean of the squared results: (25+225+3052+225+8100+7225+9025+15625+5625)/9 = root (5458.5) = 73.88
So Standard deviation=73.88

Since error percentage is 5% so confidence level will be 95% and hence the Crititcal value is 1.96
p= Type I error, (alpha), is defined as the probability of rejecting a true null hypothesis
P(x) = (1/(sqrt(2)))e-(x-m)2 / (22)
Probability density function:   0.00274250
He can reject null hypothesis

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