The confidence intervals discussed thus far give both a lower confidence bound and an upper confi-dence bound for the parameter being estimated. In some circumstances, an investigator will wantonly one of those two types of bounds. For example, a psychologist may want only an upperconfidence bound for true average reaction time to a particular stimulus.Suppose you work on a large-sample n from a population with known variance o2 so that the CLTcan be applied. i.e. the quantityXx-μo/√nis approximately normal. Prove (derive) that a (1 - a)100% upper confidence bound for u is of theform(-00, X + 2a- — /m)

X-μσn has normal distribution z

Answered: The confidence intervals discussed thus…

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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Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.4 parts/million (ppm). A researcher believes that the current ozone level is not at the normal level. The mean of 1090 samples is 4.3 ppm. Assume the variance is known to be 1.44. Does the data support the claim at the 0.05 level? Step 1 of 5: Enter the hypotheses: Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places. Step 3 of 5: Specify if the test is one-tailed or two-tailed. Step 4 of 5: Enter the decision rule. Step 5 of 5: Enter the conclusion.
A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Five hundred people are screened at a clinic during the first year the new test is implemented. Assume the true prevalence of Lyme disease among clinic attendees is 10%. Calculate the predictive value of a positive test.
Fill in the Blank Question 3 If one or more of the relevant predictor variables are excluded, then the resulting OLS estimators are biased. The extent of the bias depends on the degree of the between the included and the excluded predictor variables.
It is assumed that standardized test scores should be correlated with students' classroom performance. One would expect that students who consistently perform well in the classroom (on tests, quizzes, etc.) would also perform well on a standardized test scored from 0-100 (with 100 indicating high achievement). A teacher decides to examine this hypothesis. At the end of the academic year, she collects the following data for her (admittedly small) class: Standardized test score Overall GPA 56 1.8 1 73 2.6 2 78 2.9 3 83 2.9 4 85 3.0 5 rows x 2 columns What is your best guess for the expected GPA of a student who scored a 88 on the standardized test? number (rtol=0.01, atol=0.0001) Determine a 95% confidence interval for the expected GPA of a student who scored a 76 on the standardized test. Ib number (rtol=0.01, atol=0.0001) ub number (rtol=0.01, atol=0.0001)
In the US, 42.3% of all people have type O blood, 40.8% have type A blood, 12% have type B blood and 4.9% have type AB blood. A researcher wants to see if the distribution of blood type is different for millionaires. The table below shows the results of a random sample of 897 millionaires. What can be concluded at the significant level of a = 0.1. For this study, we should use [x²GOF-Test Your friend Henry helped you with the null and alternative hypotheses... Ho: The distributions of blood types are the same between the general population and the millionaires. H₁: The distributions of blood types are NOT the same between the general population and the millionaires. You drew 897 samples, and the observed frequencies are recorded below. Please complete the table (round answers to at least 4 decimal places). Blood Type 0 A B AB Observed Frequency 375 The degree of freedom = 366 104 52 The test-statistic for this data = The p-value for this sample= Expected Frequency (Please show your…
What are the independent and dependent variables for the following examples? What statistical test would you use for each of the following scenarios? What would you set your alpha-level at? Sally wants to examine whether there is a difference in muscular strength between participants who engaged in an 8-week resistance training program and participants who engaged in an 8-week endurance training program. The participants only took part in one of the 8-week programs, not both. What test would she use to determine whether the differences in muscular strength are significant? Why?
The next six questions refer to the following scenario: A random sample of 25 students were asked to self-identify as "statistics-lovers" or "statistics-adorers." 16 students self-identified as "lovers" and 9 students as "adorers." Below table summarizes the mean of a statistics test and standard deviation that was given after the self-identification. Test the following hypothesis at alpha=5% (0.05). HO: Mean Statistics Lovers = Mean Statistics Adorers HA: Mean Statistics Lovers Mean Statistics Adorers You can assume equal variance.
Time to Complete the Course Right 45 47 50 49 50 50 48 44 Left | 45 | 43 48 47 50 52 | 44 42 Assume a Normal distribution. What can be concluded at the the a = 0.01 level of significance level of significance? For this study, we should use t-test for the difference between two dependent population means a. The null and alternative hypotheses would be: p1 p2 Ні: p1 p2 b. The test statistic t v v = 1.199 (please show your answer to 3 decimal places.) c. The p-value = [1338 your answer to 4 decimal places.) d. The p-value is > va e. Based on this, we should fail to reject f. Thus, the final conclusion is that ... * (Please show v the null hypothesis. O The results are statistically insignificant at a = 0.01, so there is insufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over
Solve question #9 for part D only.
the data support the claim that the average ACT composite score of students from this students is randomly selected from a local high school with an X = 23 and s = 5.2. Do ACT composite scores are normally distributed with a u = 21. A sample of 25 students is randomly selected from a local high school with an X= 23 and s =5.L.D high school is different than 21 on the ACT composite score, using x = .05?
USE THE 8-STEP HYPOTHESIS TESTING Refer to the study by Carter et al. [A-9], who investigated the effect of age at onset of bipolar disorder on the course of the illness. One of the variables studied was subjects' family history. Table 3.4.1 shows the frequency of a family history of mood disorders in the two groups of interest: early age at onset (18 years or younger) and later age at onset (later than 18 years). Family History of Mood Disorders Early ≤ 18(E) 28 19 41 53 Later > 18 (L) 35 38 44 60 141 Total 63 57 85 113 Negative (A) Bipolar disorder (B) Unipolar (C) Unipolar and bipolar (D) Total 177 318 Source: Tasha D. Carter, Emanuela Mundo, Sagar V. Parkh, and James L. Kennedy, "Early Age at Onset as a Risk Factor for Poor Outcome of Bipolar Disorder," Journal of Psychiatric Research, 37 (2003), 297-303. Can we conclude on the basis of these data that subjects 18 or younger differ from subjects older than 18 with respect to family histories of mood disorders? Let a = .05.
Suppose we wanted to test the hypothesis that a control group of cancer patients (Group 1) would report higher mean pain ratings than an experimental group receiving special massage treatments (Group 2). Using the following information, compute a t statistic for independent groups: Group 1: Mean = 76.5 Standard deviation = 13.1 N =20 Group 2: Mean = 72.1 Standard deviation = 14.7 N =20 What are the degrees of freedom and the value of t? Write a null and alternative hypothesis, Using α = .01 for one-tailed test, is this t statistically significant?

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