In October 2024
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A discrete random variable X is believe to follow a binomial distribution b(x; 5, p). If P(X = 0) = 243/1024, then find P(X = 3).
Is it possible to have a Binomial Distribution in the following cases:
i. Mean = 5 and Variance = 2.5
ii. P(X = – 2) = 0.1467
iii. P(X less than or not equal to 1) = 0.18
iv. Three parameters i.e. n, p and q
v. P(X = 1) = 0.35
vi. P(X Greater than or equal to 1) = 1.27
vii. .P(X = 3.5) = 0.19
viii. P(1 less than or not equal to X less than or not equal to 4) = 0.79.
A random sample of 81 observations is taken from a normally distributed population Y with unknown mean θ and unit variance. For testing H0 : θ = 10.1 against H1 : θ > 10.1 , the following acceptance region is used: A = { y : ӯ ≥ 9.88}. Determine the size of this acceptance region.
A certain event is believed to follow the binomial distribution. In 1024 samples of 5, the result was observed once 405 times and twice 270 times.
Calculate the probabilities p and q.
The lifetimes of a certain type of electrical components are distributed with a mean of 800 hours and standard deviation of 160 hours.If the manufacturer wishes to replace only 1 percent of the component that have the shortest life .what value should be used as the guaranteed lifetime
A. Find the finite population correction factor given the following:
(Show your solutions)
1. N=400,n=40
According to the May 16,2017 report by Pew Research, 68% of US adults say solar energy is very effective in minimizing air pollution. A sample of 240 U.S adults are surveyed. Let p
ˆ
p^ be the sample proportion of Americans who believe solar energy is very effective in minimizing air pollution.
- What is the population proportion? Answer (decimal form)
- What is the sample size? Answer
- What is the mean of the sampling proportion? Answer
- What is the standard deviation of the sampling proportion? Answer
(Round to 4th decimal place)
(a) Identify the claim and state H0 and Ha. (b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning. (c) Choose one of the options. If convenient, use technology. Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic. Option 2: Find the appropriate standardized test statistic and the P-value. (d) Decide whether to reject or fail to reject the null hypothesis. (e) Interpret the decision in the context of the original claim.
7. A researcher claims that the mean age of the residents of a small town is more than 32 years. The ages (in years) of a random sample of 36 residents are listed below. At a = 0.10, is there enough evidence to support the researcher’s claim? Assume the population standard deviation is 9 years.
41 33 47 31 26 39 19 25 23 31 39 36
41 28 33 41 44 40 30 29 46 42 53 21
29 43 46 39 35 33 42 35 43 35 24 21
(a) Identify the claim and state H0 and Ha.
(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning.
(c) Choose one of the options. If convenient, use technology.
Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic.
Option 2: Find the appropriate standardized test statistic and the P-value.
(d) Decide whether to reject or fail to reject the null hypothesis.
(e) Interpret the decision in the context of the original claim.
4. A research center claims that more than 55% of U.S. adults think that it is essential that the United States continue to be a world leader in space exploration. In a random sample of 25 U.S. adults, 64% think that it is essential that the United States continue to be a world leader in space exploration. At a = 0.05, is there enough evidence to support the center’s claim?
For this test, do the following.
(a) Identify the claim and state H0 and Ha.
(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning.
(c) Choose one of the options. If convenient, use technology.
Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic.
Option 2: Find the appropriate standardized test statistic and the P-value.
(d) Decide whether to reject or fail to reject the null hypothesis.
(e) Interpret the decision in the context of the original claim.
3. A travel agent says that the mean hotel room rate for a family of 4 in a certain resort town is at most $170. A random sample of 33 hotel room rates for families of 4 has a mean of $179 and a standard deviation of $19. At a = 0.01, is there enough evidence to reject the agent’s claim?
