**Hypothesis Testing: Reaction Time Analysis**We aim to conduct a hypothesis test to determine if the population mean reaction time for drivers, after brake application by the driver in front, is less than 1.8 seconds. We selected a random sample, which has a mean of 1.9 seconds and a standard deviation of 0.4 seconds.**Sampling Scenarios and Test Statistics**For each sampling scenario, select an appropriate test statistic for testing the population mean hypothesis, then calculate the statistic. Round your answers to two decimal places.**(a)** The sample size is 90, from a non-normally distributed population with a known standard deviation of 0.40.- Options for test statistic: - \( z = \) - \( t = \) - It is unclear which test statistic to use.**(b)** The sample size is 16, from a normally distributed population with an unknown standard deviation.- Options for test statistic: - \( z = \) - \( t = \) - It is unclear which test statistic to use.**Instructions:**1. Determine and select whether a \( z \)-test or a \( t \)-test is appropriate based on the sample size and population information.2. Use the provided sample mean, population mean under null hypothesis, sample standard deviation, and sample size to calculate the chosen test statistic.3. Enter the calculated value in the provided space.This activity helps in understanding when to apply different statistical tests and how to compute them given various data scenarios.

given data, sample mean =1.9sample standard deviation =0.4claim:μ<1.8we have to find out the type…

Answered: We want to conduct a hypothesis test of…

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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We want to conduct a hypothesis test of the claim that for middle-aged adults the population mean of their cholesterol levels is less than 195.7 mg a random sample of such levels. The sample has a mean of 192.7 and a standard deviation of 19 dL mg dL (a) The sample has size 14, and it is from a normally distributed population with an unknown standard deviation. 0:= 0 O For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places. O =0 O It is unclear which test statistic to use. (b) The sample has size 20, and it is from a normally distributed population with a known standard deviation of 19.1. z = 0 O o t=0 O It is unclear which test statistic to use. mg dL X We choose S
A sample of size n = 36 is drawn from a population whose standard deviation is σ = 15.6. The sample mean is x = 94.5. Construct a 95% confidence interval.
The population of healthy female adults, the mean red blood cell count (RBC) is 4.8 (millions of cells per cubic millimeter of whole blood). A researcher thinks the RBC is underestimated, so she conducts a test of significance using Null Hypothesis: µ ≤ 4.8 vs. Alternative Hypothesis: µ >4.8. If the true mean RBC is 4.75 and the null hypothesis is rejected, out of the four options below, what has occured? Type 1 Error, Type 2 Error, No error, OR can’t tell without knowing the degrees of freedom?
The null and alternate hypotheses are: He: P₁ =H₂ H₁ H₁ #P₂ A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. The population variances are assumed to be equal. At the 0.10 significance level, is there a difference in the population means? a. Is this a one-tailed or a two-tailed test? O One-tailed test. OTwo-tailed test. b. State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) The decision rule is to reject H0 if t
You are interested in testing whether the average age of household heads is higher in the suburbs than in inner city neighbourhoods. A survey is conducted, and the following results are obtained. In the suburbs, the household heads of the 45 households surveyed had a mean age of 44 with a standard deviation of 15. In the inner city, the mean age of the 40 household heads surveyed was 38 with a standard deviation of 13. Assuming that the populations from which these samples were drawn have equal variances, can you conclude that the difference between the two means is significant at the 95% level of confidence? (a) Write in words and symbols the null and research hypotheses. (b) Assuming the variances of the populations are equal, calculate the value of the Pooled Variance Estimate (PVE). (c) Calculate the value of the standard error for the difference between the two means.
Two samples were drawn independently from two normal populations. Sample 1: 11.6, 11.35, 10.1, 10.85, 10.35, 10.6, and 11.1.Sample 2: 5.85, 8.85, 9.85, 11.85 and 7.85.Test to determine whether the means of the two population differs (use α=0.05).
If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic? Question 3 options: The two samples both have n = 15, with sample variances of 20 and 25. The two samples both have n = 15, with variances of 120 and 125. The two samples both have n = 30, with sample variances of 20 and 25. The two samples both have n = 30, with variances of 120 and 125.
Suppose we have two normal populations denoted A and B, and we want to compare their population variances by estimating the ratio: variance of population B divided by variance of population A. We have an independent random sample of size 15 from population A and an independent random sample of size 9 from population B. The sample variance for population B turns out to be 30 percent larger than that for population A. What is the 99 percent confidence interval for the ratio: population variance of population B divided by population variance of population A? Use stattrek.org for finding the needed critical values.
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test? Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. Determine the critical region using a one-tailed test with alpha = .05. Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). Based on your analysis, is there a relationship between the drug and attention span?
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 436 gram setting. Based on a 20 bag sample where the mean is 433 grams and the variance is 121, is there sufficient evidence at the 0.025 level that the bags are underfilled? Assume the population distribution is approximately normal. Step 1 of 5 : State the null and alternative hypotheses.
We want to conduct a hypothesis test of the claim that the population mean time it takes drivers to react following the application of brakes by the driver in front of them is more than 2.3 seconds. So, we choose a random sample of reaction time measurements. The sample has a mean of 2.2 seconds and a standard deviation of 0.5 seconds. For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places. (a) The sample has size 12, and it is from a normally distributed population with an unknown standard deviation. O z = 0 %3D Ot= It is unclear which test statistic to use. (b) The sample has size 17, and it is from a population with a distribution about which we know very little. O z t =|| D- It is unclear which test statistic to use.

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