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
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
K A population has a mean μ = 134 and a standard deviation o = 26. Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 59. σ- The mean is μ- =, and the standard deviation is o- = (Round to three decimal places as needed.) X Z-
Test the claim below about the mean of the differences for a population of paired data at the level of significance a. Assume the samples are random and dependent, and the populations are normally distributed
Treatment Sham Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure u of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. H1 H2 In 10 10 0.56 0.37 0.97 1.45 O B. Ho: H1 + H2 O A. Ho: H1 = H2 H1: H1 # H2 H1: H1 H2 H1: H12 H2 The test statistic, t, is|. (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. V the null hypothesis. There V sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. Is it valid to argue that magnets might appear to be effective if the…

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