A researcher wants to estimate the average time a person spends commuting to Boston. The researcher chooses a random sample of 22 people and finds that their average commute is 49 minuteswith a standard deviation of 19 minutes. Assume that commute times are normally distributed.(a) Why are we allowed to assume that the sampling distribution in this problem is approximately normal?O The margin of error is unknown.O The population standard deviation is known.O The population is normally distributed.O The sample size is large enough.(b) Which distribution should be used to find the critical value?O The t-distribution because o is unknown.O The t-distribution because the sample size is small.O The Z-distribution because o is known.O The z-distribution because the sample mean is large enough.(c) Construct a 90% confidence interval for the true average commute time. Round your answers to two decimal places.lower limitupper limitmargin of error

Given: Sample size, n is 22 Sample mean, x¯=49 Sample sd, s is 19

Answered: (a) Why are we allowed to assume that…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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What would happen to the sampling distribution if you increased the size of the samples taken from the population? O The center of the sampling distribution will get further away from the parameter O The spread of the sampling distribution will get larger O The center of the sampling distribution will get closer to the parameter O The spread of the sampling distribution will get smaller
View Policies Current Attempt in Progress Use a t-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d = X¡ - X2. Test Ho : ua = 0vs H. Ha > 0 using the paired data in the following table: Situation 1 125 156 140 175 153 148 180 135 168 157 Situation 2 120 145 142 150 160 148 160 142 162 150 Give the teststatistic and the p-value. Round youranswer for the test statistic to two decimal places and your answer for the p-value to three decimal places. test statistic = p-value = eTextbook and Media MacBook Air
find normal distribution P(1 < Z < 2) = P(Z < 2) − ____________________.
Which of the following is true about sampling distributions? O Shape of the sampling distribution is always the same shape as the population distribution, no matter what the sample size is. O Sampling distributions are always nearly normal. Sampling distribution of the mean is always right skewed since means cannot be smaller than 0. O Sampling distributions get closer to normality as the sample size increases.
The t distribution is applicable when Group of answer choices the population has a mean of less than 30 the sample standard deviation is used to estimate the population standard deviation the variance of the population is known the standard deviation of the population is know
The graph of a normal curve is given below. -7-4 -1 2: 8 11 X The value of the mean (U) is and the value of the standard deviation (O) is
Activity: SAMPLING DISTRIBUTIONS OF THE SAMPLING MEANS A. Directions: Consider the given, then analyze and solve what is asked in each number. Giyen: A finite population of numbers has a size N = 4. The population consists of values 12, 14,16 and 18. 1. Determine the mean, standard deviation, and variance of the population. µ : 02 : Table 3.1 : Complete the detaiis in Table 3.1 Sample Mean No. Sample a. obtain a random sample of size n = 2 without replacement and make sure that all possible sample sets are listed b. compute the mean of each sample 3. Construct the sampling distribution of the sample means. 4. Compute the mean and standard deviation of the sampling distribution of the sample means. Use table 3.2 for nos. 3 to 4 'able 3.2 Sample Mean X p(X) (X) * p(X) (X – µx)2 * p(X) Ox² = OX= 5. Compare the mean, variance, and standard deviation of the sampling distribution of the sample means with the mean, variance, and standard deviation of the population. What generalization can be…
For the population proportion is… (select answer) Skewed right Uniform Approximately normal Skewed left With the… (select answer) True population proportion True population mean True population standard deviation As it’s… (select answer) Proportion Mean Standard deviation
Which of the following statements is FALSE regarding the t distribution The t distribution for df = 4 is flatter and more spread out than the t distribution for df = 20 The t distribution is symmetrical The standard deviation of the t-distribution is one The mean of the t-distribution is zero As the degrees of freedom increase, the t-distribution approaches the normal distribution
Sampling Distribution: Suppose a very large number of random samples of size 25 are selected from a population with a known mean and standard deviation. If the mean of all the samples is found to be 300 and the standard deviation of these samples is found to be 20, what is the true mean and true standard deviation of the distribution from which the samples are drawn?
The probability distribution of a random variable Y is given below. Y = y 2 4 6 8 P (Y = y) 0.1 0.3 0.4 0.2 1. Find the probability that Y is within one standard deviation of its expected 2. Explain why Y does not have a discrete uniform distribution. A population is normally distributed with µ = 138 and sigma = 21. Given a simple random sample of size n = 25, determine the probability that the sample mean, X¯ , will be less than 128.

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