14) Arsenic is an element that can naturally get into local water supplies. The maximum safe level of arsenic in water is assumed to be 10 parts per billion (ppb). A sample of n=35 homes were sampled for tap water, and the sample mean arsenic level was found to be 9.72 ppm. If the population standard deviation is assumed to be 0.55 ppb, then: (a) write the null and alternate hypotheses to test to see if the mean concentration of arsenic in tap water is less than 10 ppb; b) Carry out a one-sample z-test at the 5% significance level Instead of a z-test, repeat this test using the p-value approach. All you need to do is calculate the p-value. Then state whether you would accept or reject the null hypothesis at the 5% level based on the p-value. No need to re-write everything else.

14) Arsenic is an element that can naturally get into local water supplies. The maximum safe level of arsenic in water is assumed to be 10 parts per billion (ppb). A sample of n=35 homes were sampled for tap water, and the sample mean arsenic level was found to be 9.72 ppm. If the population standard deviation is assumed to be 0.55 ppb, then: (a) write the null and alternate hypotheses to test to see if the mean concentration of arsenic in tap water is less than 10 ppb; b) Carry out a one-sample z-test at the 5% significance level Instead of a z-test, repeat this test using the p-value approach. All you need to do is calculate the p-value. Then state whether you would accept or reject the null hypothesis at the 5% level based on the p-value. No need to re-write everything else.

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Description: 10:05 AM Sat Dec 19* 64%+: 014) Arsenic is an element that can naturally get into local water supplies. The maximum safelevel of arsenic in water is assumed to be 10 parts per billion (ppb). A sample of n = 35homes were sampled for tap water, and th

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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I. A study reports that teenagers spend 27 hours a week online (www.telegraph.co.uk). A researcher wanted to check if this claim is true. A random sample of 200 teenagers taken showed that they spend an average of 25.7 hours per week online with a standard deviation of 8.2 hours. Perform a hypothesis test with the alternate hypothesis that teenagers spend less than 27 hours per week online. Use c = 0.05. Perform all of the steps outline in your notes and write a complete conclusion in words. Assume the distribution of hours spent online is normally distributed.
. The acceptable pollutant level in a county is 7.8 g/cc. A researcher believes that their portion of the county has a level higher than this, and takes a sample of 70 observations. The sample mean is 8.8 g/cc, with a standard deviation of 3.1. Set up the null and alternative hypotheses, and use alpha = 0.05. Test the null hypothesis and give the p-value (4).
We want to test hypotheses concerning the population mean. The following data is given: x¯¯¯=82,n=15, the population is normal with a standard deviation of 5.2. If we are to test the following hypothesis: H0:μ=85 Ha:μ<85 with a significance level of 0.05, the p-value suggests we a.) accept the alternate hypothesis b.) Fail to reject the null hypothesis c.) reject the null hypothesis d.) do nothing, let someone else get paid to figure it out.
If random samples, each with n = 16 scores, are selected from a normal population with µ = 100 and σ = 20, how much difference, on average, should there be between a sample mean and the population mean?
An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).
3. A fitness center claims that its members lose an average of 12 pounds or more the first month after joining the center. An independent agency that wanted to check this claim took a sample of 45 members and found that they lost an average of 10 pounds within the first month with standard deviation of 3 pounds. Find the p-value for this test. What will your decision be if a =0.05? Solution: Step 1: State the hypotheses. Step 2: The level of significance and critical region. a =, and zeritical = Step 3: Compute for the value of one sample z test. zcomguted = and p-value = Step 4: Decision rule. Step 5: Conclusion.
The population mean ACT composite score in 2015 was 20.8 points, with population standard deviation 5.6 points. The population size of number of tests taken in 2018 is extremely large (more than 1 million). Consider all samples of size 40 tests. find A and B
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Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 32 PlayStation users had an average age of 33.7 years while a random sample of 36 Xbox users had an average age of 35.6 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.7 and 3.5 years, respectively. Sony would like to set α = 0.05. The p-value for this hypothesis test would be
1) Your instructor tells you that past average scores for the final exam are 75%. But this semester he has been using online quizzes to help your class better prepare for the final. Your class scored the following on the final exam: mean= 80% with a 10% standard deviation. There are 49 people in your class. Using a one-sample t test, what is your t score for this class? Assuming α = .05, did the online quizzes help your class perform better?
2. Suppose that a random variable X follows a normal distribution with unknown mean u but a known standard deviation of 30. We're interested in testing: Ho: = 75 versus Ha: < 75. Using a = 0.01, find the sample size n necessary to achieve the power of the test to be 0.90 when the value of the mean is 65 under the alternative hypothesis.
In order to test the claim that the mean drive speed (Km/hr) of adults in a known highway in a city is at most 75 Km/hr, a sample of 40 adult drivers was taken and resulted a sample mean of 85 Km/hr. If the population standard deviation is 35 Km/hr, perform the test with a level of significance a = 0.05 using the P-value approach. 1. The mull and alternative hypotheses are A. Ho : u 75 and H : u 75 D. Ho : 2 75 and H, : p< 75 2. Test statistic value = (approximate to two decimal places) D. 1.81 A. -1.81 B. 0.29 C. 0.29 3. P-value = A. 0.0702 (approximate to four decimal places) B. 0.1404 C. 0.9298 D. 0.0351 4. The decision of the test: A. Reject Ho, there is a strong evidence that the adults mean drive speed is less than 75 Km/hr. B. Do not reject Ho, there is no evidence that the adults mean drive speed is more than 75 Km/hr. C. Reject Ho, there is a strong evidence that the adults mean drive speed is more than 75 Km/hr. D. Do not reject Ho, there is a strong evidence that the adults…