If our sample size is small (n<30), we can assume the sample mean has a normal distribution. True O False
Q: The difference between two sample means follows a normal distribution if both populations follow a…
A: True We can find it by using the Central limit theorem. By the theorem, difference in sample means…
Q: When the sample size is over 30, when would the t test be used instead of normal distribution?
A: A t test will be used, when the population standard deviation is unknown and either the population…
Q: size
A: As per the weak law of large numbers, every distribution tends to normal distribution as we increase…
Q: A simple random sample of size 17 is taken from a population with unknown standard deviation. A…
A: The following assumptions are required for the small sample confidence interval about mean to be…
Q: Samples of size 50 are taken. Can you assume that the distribution for x is normal
A: The given sample size is 50.
Q: If all normal distributions have the same shape, how do they differ?
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Q: Write TRUE if the statement is unconstitutionally true, FALSE if otherwise. 1. If the population…
A: By the assumption of normality, the distribution of sample means (with the assumption that each…
Q: normal distribution has a mean of mu = 40 with sd =5. What is the probability of sampling an…
A: we want to find probability of sampling an individual with a score greater than 48
Q: Given that z is a standard normal random distribution, find z for each situation The area to the…
A: The area to the right of z is 0.1314 is obtained below:From the given information, the probability…
Q: When simple random samples are drawn from a population that is normally distributed, the sampling…
A: According to the definition of Central limit theorem, the sampling distribution of the sample means…
Q: True or False: If the population distribution given is normally distributed, then the sampling…
A: The Central Limit theorem suggests that if the original population is normally distributed, then the…
Q: A normal distribution is unimodal distribution. It means that a. Mean, Median and Mode are equal b.…
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Q: Write TRUE if the statement is unconstitutionally true, FALSE if otherwise. 1. If the population…
A: Given the statement, If the population follows a Normal distribution, then for n = 1, X follows a…
Q: A normal distribution has a mean of u = 70 with o =3. What is the probability of sampling an…
A: We have find givan normal distribution...
Q: There are many different ways to determine whether or not a data set has a normal distribution. O…
A: Find your answer below
Q: The shape of the T-distribution curve is wider than the normal curve because, O a. it has more…
A: If population standard deviation is known and large sample size i.e, n > 30 then we use z-…
Q: In a parametric statistical test a normal distribution and equal variance is assumed. Select one:…
A: In a parametric statistical test a normal distribution and equal variance is assumed.
Q: Suppose that 40% of Americans drink soda every day. Amy, a researcher at a local university, takes a…
A: Answer:- Here the random variable X has binomial distributionThe sample size is: Probability of…
Q: It would be appropriate to use the normal approximation to the binomial distribution in a situation…
A: The following information has been provided: n=20p=0.80
Q: For the distribution of sample means to be normally shaped, it must be derived from samples of at…
A: We have given that the distribution of the sample means to be normally shaped, it may be derived…
Q: True or False 1. The sum of the probabilities of all values of the random variable must be equal to…
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Q: If x has a normal distribution with mean u=15 and standard deviation o=3, describe the distributin…
A: Given information, μ=15σ=3 Given sample sizes, n=4, n=16, n=100. The sampling distribution for n=4:…
Q: How do we know if a null distribution is normal? Does it have to explicitly say that the population…
A: Points on the sampling distribution of the sample mean: If the true population distribution of a…
Q: Let the random variable X follow a normal distribution with mean = 120 and variance = 72.25. Find…
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Q: (a) 60% of the distribution below it, (b) 75% of the distribution below it, (c) 80% of the…
A: standard normal distribution Z~N(0,1) we have to find value of z such that (a) 60% of the…
Q: Nonparametric test is a design to counter the non-normal distribution type of data. O True
A: Nonparametric test: The nonparametric tests are used if the population distribution is not known.…
Q: What important theorem in statistics implies that, for a large sample size, the possible sample…
A: Central limit theorem for proportion: As the sample size increases, the sampling distribution of…
Q: A normal population distribution has a sample mean of u=65. What is the expected value of the mean…
A: The objective is to find the expected value of the mean. From the available information , A normal…
Q: The distribution of the variance (Chi-Square distribution) becomes more like a normal distribution…
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Q: Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that…
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- When should a s distribution be used? When there are how many cases in a sample? When should a t distribution be used? When there are how many cases in a sample?Supp ok se you did not know that x had a normal distribution. Would you be justified in saying that the distribution is approximately normal if the sample size were n=12☐True ☐FalseA normal distribution is necessarily unimodal.
- Assume that the average score on a statistical test is 8.5 and the variance is 2. The test was on the lighter side and the score distribution was very skewed (left skewed). What probability distribution is it reasonable to assume that the average grade of 3 randomly selected students who take the exam follows? 1. Normal distribution with mean 8.5 and variance 2. 2. Normal distribution with an average of 8.5 and a variance of 2/3. 3. Poisson distribution with an average of 8.5 and a distribution of 8. 4. The probability distribution cannot be predicted from the information provided.Consider a hypothesis test of difference of means for two independent populations x1 and x2. Suppose that both sample sizes are greater than 30 and that you know ?1 but not ?2. Is it standard practice to use the normal distribution or a Student's t distribution? Use the Student's t distribution because both sample sizes are greater than 30. Use the normal distribution because we do not know ?2. Use the normal distribution because both sample sizes are greater than 30. Use the Student's t distribution because we do not know ?2.The Central Limit Theorem tells us that the distribution of the sample mean is Normal, regardless of the population distribution or the size of the sample True or false
- When the degrees of freedom are nearing infinity, the chi-squared distribution is exactly a normal distribution O True O FalseThe distribution used for small sample size (n<30) changes based on the size of the sample. True FalseA normal distribution has a mean of u = 45 with o =5. What is the probability of sampling an individual with a score greater than 49?