Analyses of drinking water samples for 100 homes in each of two different sections of a city gave the following means and standard deviations of lead levels (in parts per million): Section 1: n1 = 100, x¯1 = 34.1, s1 = 5.9, Section 2: n2 = 100, x¯2 = 36.0, s2 = 6.0. (a) Calculate the test statistic and its p-value to test for a difference in the two population means. Use the p-value to evaluate the statistical significance of the results at the 5% level. (10 pts) (b) Use a 95% confidence interval to estimate the difference in the mean lead levels for the two sections of the city. (10 pts) (20 pts)
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Analyses of drinking water samples for 100 homes in each of two different sections of a...
Analyses of drinking water samples for 100 homes in each of two different sections of a city gave the following means and standard deviations of lead levels (in parts per million): Major Section 1 Section2 32 38.1 5.7 5.8 Find a 95% confidence interval for lower limit upper limit- 1712 Suppose that the city environmental engineers will be concerned only if they detect a difference of more than 5 parts per million in the two sections of the city. Based...
Two sections of 70 Introductory Sociology students were taught with one section using no text and the other section using a popular introductory text. At mid-term, the same test was given to both sections with the following results: No Text Popular Text n1=70 n2=70 1=75 2=71 S1=8 S2=10 a) Test for the significance of the difference between two population means (set α (alpha) =.01 level). b) Calculate the effect size (ES) and determine its...
Independent random samples selected from two normal populations produced the sample means and standard deviations shown to the right. a) Assuming equal variances, conduct the test Ho: (u1-u2)=0 against Ha: (u1-u2)=/=0 using a=0.05 b) Find and interpret the 95% confidence interval for (u1-u2) Sample1: n1=17, x1=5.9, s1=3.8 Sample2: n2=10, x1=7.3, s2=4.8
There are two sections of statistics, one in the morning (AM)
with 24 students and one in the afternoon (PM) with 27 students.
Each section takes an identical test. The PM section, on average,
scored higher than the AM section. The results are summarized in
the table below.
Necessary information:
n
x
s2
s
PM (x1)
27
80.8
277.5
16.66
AM (x2)
24
70.9
250.3
15.82
The Test: Test the claim that the PM section did
significantly better than the...
Question 5 3 pts The following data concerns a randomized controlled trial. Two groups of 100 men with systolic blood pressure in the 120 to 130 range and diastolic blood pressure in the 80 to 90 range are treated to reduce the “pre-hypertensive” state. The men are in the age range 30 to 40 years. The control group 1 is given placebo and the experimental group 2 is given a treatment.to reduce blood pressure. Assume the standard deviations are equal...
Question 3 4 pts Acme Products manufactures widgets. It has two machines which produce widgets. It is desirable that both machines produce widgets of the same dimensions. At regular time intervals Acme's quality control tests the widgets from both machines. The last test produced the following results. In this context sM is the sample mean. SM1 = 5.61 S1 = 1.07 n1 = 100 SM2 = 5.89 S2 = 1.26 n2 = 100 Do the machines produce different sized widgets?...
Question 5 3 pts The following data concerns a randomized controlled trial. Two groups of 100 men with systolic blood pressure in the 120 to 130 range and diastolic blood pressure in the 80 to 90 range are treated to reduce the “pre-hypertensive” state. The men are in the age range 30 to 40 years. The control group 1 is given placebo and the experimental group 2 is given a treatment.to reduce blood pressure. Assume the standard deviations are equal...
a) Use the t-distribution to find a confidence interval for a difference in means μ1-μ2 given the relevant sample results. Give the best estimate for μ1-μ2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed. A 90% confidence interval for μ1-μ2 using the sample results x¯1=8.8, s1=2.7, n1=50 and x¯2=13.3, s2=6.0, n2=50 Enter the exact answer for the best estimate and round your answers for the margin...
There are two sections of statistics, one in the afternoon (PM) with 30 students and one in the morning (AM) with 22 students. Each section takes the identical test. The PM section, on average, scored higher than the AM section. The scores from each section are given in the table below. Test the claim that the PM section did significantly better than the AM section, i.e., is the difference in mean scores large enough to believe that something more than...
1) Consider two independent random samples of sizes n1 = 14 and n2 = 14, taken from two normally distributed populations. The sample standard deviations are calculated to be s1= 1.98 and s2 = 5.71, and the sample means are x¯1=-10.2and x¯2=-2.34, respectively. Using this information, test the null hypothesis H0:μ1=μ2against the one-sided alternative HA:μ1<μ2, using Welch's 2-sample t Procedure for independent samples. a) Calculate the value for the t test statistic. Round your response to at least 2 decimal...