When constructing a confidence interval for μwhen σis known, we assume that we have a simple random sample, that σis known, and that either the sample size is large or the population is approximately normal.  Why is it necessary for these assumptions to be met?

Q: Suppose that you take 1000 simple random samples from a population and​ that, for each​ sample, you…

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Q: For a two-tailed test at 99% confidence based on a sample of size 20 with unknown population…

A: Confidence interval is a range of values it contains the true population parameter with specified…

Q: A random sample of size n1=25, taken from a normal population with a standard deviation σ1=5, has a…

A: Givensample size(n1)=25standard deviation(σ1)=5Mean(x1)=80sample size(n2)=36standard…

Q: A simple random sample of size n is drawn from a population that is normally distributed. The…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: We are interested in finding a 99% confidence interval on K. A sample of size 39 provided a point…

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Q: Let a random sample of size 17 from the normal distribution N(μ, σ2) yieldx = 4.7 and s2 = 5.76.…

A: Consider the random sample size of n=17 from the normal distribution N(μ,σ2)yield  x=4.7, s2=5.76.…

Q: Which of the following is NOT needed to compute a confidence interval  Critical t   standard error…

A: In this case, we need to find the incorrect option for the given statement.

Q: Suppose x has a normal distribution with a = 1.9. Find the minimal sample size required so that for…

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Q: A confidence interval for the difference between the means of two normally distributed populations…

A: The t-test can be used for both dependent samples and independent samples. If the variables are…

Q: The weights in grams of oranges grown in a certain area are normally distributed with mean µ and…

A: The confidence interval is (222.1, 232.1).

Q: a 90% confidence interval for for the probability of success in a Bernoulli trial with n=48

A: Confidence interval: It is defined as the range that contains the value of the true population…

Q: Suppose that 100 samples of size n = 50 are independently chosen from the same population and that…

A: The confidence interval at 100 (1 – α) % confidence level gives us an interval estimate about the…

Q: The t distribution is used to make a confidence interval for the population mean if the population…

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Q: The following results are for independent random samples taken from two populations. Suppose that we…

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Q: What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of…

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Q: Increasing the sample size will make a confidence interval a. Either wider or narrower but we cannot…

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Q: A simple random sample of size n is drawn from a population that is normally distributed. The sample…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: A simple random sample of n-15 is drawn from a population that is normally distributed. The sample…

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Q: A random sample of size n is taken from a normal population with variance 36 how large the sample…

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Q: The minimum sample size needed to construct a 95% confidence interval for u, with error not…

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Q: Suppose that you wish to obtain a confidence interval for a population mean. Under the conditions…

A: Given The Pop. sd is unknown. The pop. is normally distributed. The sample size (n) is small.

Q: A sample of size 26 has a sample variance of 100. Then a 90% Confidence Interval for o? is < o? <

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Q: The weights in grams of oranges grown in a certain area are normally distributed with mean µ and…

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Q: Let us give a 95% confidence interval estimate for the population mean. If the sample mean is 1000…

A: Given Data: Sample mean(x¯)=1000 Standard error(SE)=50   Confidence Level=95%

Q: find the critical value t of alpha over 2 used to construct  the confidence interval for a mean from…

A: It is given that n is 5 and level of significance is 0.02.

Q: The minimum sample size needed to construct a 95% confidence interval for u, with error not…

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Q: A símple random sample of size 100 has mean 15, the population variance being 25. Find an interval…

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Q: The use of the standard normal distribution for constructing a confidence interval estimate for the…

A: We have to find out correct option for given data

Q: Suppose we take a random sample, N = 64, from the Texas population of adults and find that the…

A: It is given that, Sample size, n=64 x̅=14 and σ=4 We have, Z0.05/2 = 1.96 We can find 95% confident…

Q: To construct a confidence interval for the difference between two population means ₁-₂, use the…

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Q: (b) Estimate the sample size needed if no estimate of p is available. A sample of 504 adults is…

A: Given that m.e=0.03,alpha=0.002 ( 2 ) n=?

Q: An interval estimate with a 99% confidence means that there is 0.99 probability that the population…

A: We have to interpret the confidence interval.

Q: Which of the following is not a condition for constructing a confidence interval to estimate the…

A: A condition interval to estimate the difference between two population proportion is as follow:

Q: In random, independent samples of 275 adults and 200 teenagers who watched a certain television…

A: The random variable television show follows binomial distribution. There are two samples which are…

Q: A random sample of n measurements was selected from a population with unknown mean u and standard…

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Q: If x is a value of a random variable having an exponen-tial distribution, find k so that the…

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Q: The general rule for the use of the Central Limit Theorem to reasonably assume that ¯xx¯ is normally…

A: The Central Limit Theorem states that the distribution of total or mean is approximately normal for…

Q: A simple random sample of size n is drawn from a population that is normally distributed. The…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: We can use the normal distribution to make a confidence interval for a population mean provided that…

A: We need to use the concept of normal approximation and answer given question

Q: In testing the hypotheses, Ho: H1 = P2 Vs. Ha: H1# H2 samples of size 9 are taken from each of the…

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Q: Let X1,.., Xn be a random sample from a population with Gamma(a, B) distribu- tion. If a is a known…

A: Given, xi~Gammaα,β ,i=1,2,..,n Where α is known constant and β is unknown. Here, α is the shape…

Q: A simple random sample of size n is drawn from a population that is normally distributed. The sample…

A: It is given that Sample size n = 21, 12 Sample mean M = 114 Sample SD s = 10 Level of confidence =…

Q: To construct a confidence interval for the difference between two population means u, -H2, use the…

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Q: A confidence interval is calculated after running a two-sample z-test for proportions, yielding the…

A: Givenconfidence interval is [0.01,0.14]Upper Limit = 0.14Lower limit = 0.01

Q: When constructing a confidence interval forp1-p2, and if both sample sizes are large enough: a. It…

A: Given: Sample sizes for both samples are large enough

Q: In random, independent samples of 200 adults and 300 teenagers who watched a certain television…

A: From the provided information,

Q: A random sample of size 30 from a normal population yields  = 39  and s = 4.9.  The lower bound of a…

A: Note:Hey there! Thank you for the question. In the first line, it is written “A random sample of…

Q: suppose X has a mounded-shaped distribution with a standard deviation of O= 3. Find the minimal…

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Q: (a) An article in a medical journal suggested that approximately 15% of such operations result in…

A: 15% of operations result in complication; p=0.15 Margin of error=0.03 α=0.002