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11. Q10. Assume your run the statistics to test the hypothesis and your result is 0.06, and then what will be your decision as a researcher, at P is 5%?

Chinovac Labs tried a new vaccine on 189 randomly selected individuals. From the experiment, it was determined that 104 of them developed immunity. Calculate a 95% confidence interval for the proportion p of individuals in the population for whom the vaccine would help. What is the upper bound of this interval?



6 % of the 100 students in Emmie Xi Hem International School students said that they had been late in their first-period classes. What is the upper bound of the 99% confidence interval for the proportion of students in the said school who had been late in their first-period classes?


Chinovac Labs tried a new vaccine on 126 randomly selected individuals. From the experiment, it was determined that 118 of them developed immunity. Calculate a 95% confidence interval for the proportion p of individuals in the population for whom the vaccine would help. What is the point estimate of this interval?


The Malayo Colleges Mindanao recently conducted a study analyzing the privacy management habits of teen internet users. In a group of 116 teens, 80 reported having more than 100 followers on Twitter. Find the upper bound of a 90% confidence interval for the true proportion of teens who would report having more than 100 followers on Twitter. 


Show that the function f(x,y)




X^3-y^3/x^2-y^2 (x,y) Not equal to zero




0 (x,y) =0 is continuous at (0,0)

A LED company claims that the average life of the LED light bulbs it


manufactures is 1, 500 hours with a standard deviation of 500 hours. If a random


sample of 40 bulbs is chosen, what is the probability that the sample mean will be:


a. greater than 1, 400 hours?


b. less than 1, 400 hours?

A population consists of three numbers (3,4,7). Consider all possible samples of size 2 which can be drawn from the population. Find the variance of the sampling distribution of the sample means.


If the net investment function is given by I (t) = 100e^ {0.1t} calculate

(a) The capital formation from the end of the second year to the end of the fifth year;

(b) The number of years required before the capital stock exceeds $100 000


Find the consumer's surplus at $P = 5$ for the following demand functions:

(a) P=25-2Q,

(b) P= 10/sqrt {Q} 


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