Let Y₁, Y₂,..., Y₁ denote a random sample from a normal distribution with unknown mean and unknown variance o². For testing Ho: o² = o vs. Hai o² # o, show that the a-level Likelihood Ratio Test (LRT) is equivalent to the x² test
Q: The FMA Company has designed a new type of 16 lb. bowling ball. The company knows that the average…
A: Givenμ n = 120 , xbar = 170 S2 = 100 S = 10
Q: You are comparing freshmen and seniors at your college on hours spent studying per day. You pick a…
A: First sample (male): x1-bar = 3, (s1)2 = 1.2, n1 = 11. Second sample (female): x2-bar = 2, (s2)2 =…
Q: What is the probability that V value is greater than or equal to 11.14 when sample variance V is…
A:
Q: The number of people in a car that crosses a certain bridge is a random variable x. The toll on the…
A: Let us denote: X= number of persons Y= amount of money collected The fixed charge is $2. And per…
Q: The raw materials supplied by two vendors are compared. The vendors appear to supply materials that…
A: The F-test for comparison of two population variances is used to determine whether the two…
Q: Brand A: X1 = 37,900 kilometers, s, = 5000 kilometers S1 X2 = 39,900 kilometers, Brand B: S2 = 6000…
A: Given observation
Q: Twenty five independent observations are taken from a normal distribution with mean li and variance…
A:
Q: For a standardized psychology examination, the scores have a mean of 500 and a variance of 9151. It…
A:
Q: 29 non-accounting majors and 29 accounting majors are taken from a final exam. Test at the 1% level…
A:
Q: A high school principal claims that the variance in GPA of students in the graduating class is less…
A: Given
Q: A machine makes drill bits. When the machine is operating correctly, the variance of the diameter of…
A: Null Hypothesis:H0:σ2≤0.04 inches. Alternative Hypothesis: H1:σ2>0.04 inches. Test statistic:…
Q: In the Izmir University of Economics, a professor claims that exam scores for non-accounting majors…
A: Given that, nx=26, sx2=1502.588, ny=26, sy2=468.274 The null and alternate hypothesis is,…
Q: Consider a random sample drawn from the normal distribution with mean µ and variance o². The method…
A: The statement "The Method of Moments (MOM) estimator μ for the mean of a normal distribution is the…
Q: The standard z-value of an arbitrary 16- unit sample from the normal-class population with a mean of…
A:
Q: Assume thAt scores on a standardized test are known to follow a bell shaped distribution with a mean…
A: L
Q: he lifetimes in hours of two brands of batteries follow normal distributions with means μX ,μY…
A: Given : The lifetimes in hours of two brands of batteries follow normal distributions with means μX…
Q: In a study conducted on the variance of weights of bread produced daily in a bread factory, the…
A: the average weight of 51 breads was calculated as 400gr and variance as 700. the variance of bread…
Q: A company is doing a hypothesis test on the variation of quality from two suppliers. They believe…
A: Given that Sample sizes n1=37 , n2=29 Standard deviation s1=4.2045 s2=9.6752 Level of significance…
Q: The scores on a placement test given to college freshmen for the last five years are approximately…
A:
Q: A survey aims to compare the average reaction times (in seconds) of men (group A) and women (group…
A: Given the average reaction times (in seconds) of men (group A) and women (group B) to a certain…
Q: Independent random samples of the heights of adult males living in two countries yielded the…
A: The question is about hypothesis testingGiven :Randomly selected no. of adult males from country 1 (…
Q: пуро may mode. Select the correct symbols in the order they appear in the problem. Ho: 0₁² Select an…
A: Answer:- Given, For supplier 1, sample size (n1) = 25 Standard deviation (S1) = 8.448 For supplier…
Q: For tests of Homogeneity of Variance the preferred outcome is to reject the Null hypothesis. True…
A:
Q: A sample of final exam scores is normally distributed with a mean equal to 20 and a variance equal…
A:
Q: (b) There is a 99% confidence interval for the weight loss of men over the age of 30 after camping…
A:
Q: A random sample of 23 bags of apples (marked as 10 pounds each) received by a large grocery chain…
A: Solution: State the hypotheses. Null hypothesis: That is, the true mean of all bags is not less…
Q: A survey aims to compare the average reaction times (in seconds) of men (group A) and women (group…
A: Given the average reaction times (in seconds) of men (group A) and women (group B) to a certain…
Q: A study shows that running increases the percent resting metabolic rate (RMR) in older women. The…
A:
Q: For a randomly chosen adult staying in Condominium Merak, X represents the time, in minutes, spent…
A: X: Time (in mins) spent per week exercising in the gym. Y: Time (in mins) spent per week jogging. X…
Q: ds the data for the Analysis of Variance (ANOVA). If she reported the test statisti .1 "hat is the…
A: Given For the given scenario of ANOVA We have Number of groups=k=5
Q: A company is doing a hypothesis test on the variation of quality from two suppliers. They believe…
A:
Q: There is a 99% confidence interval for the weight loss of men over the age of 30 after camping for a…
A:
Q: The blood pressure and weight of Jellystone Park bears are correlated with and .6 is the correlation…
A: The provided information is: Average blood pressureY¯=150 A variance of blood pressureσ2y¯=100 The…
Q: A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of…
A: Given Information: Brand A: Sample size n=16 Sample mean x¯1=34,900 Sample standard deviation…
Q: Two samples, each with n = 10 participants, have a pooled variance, sp2 = 180. What is the estimated…
A: From the provided information, Sample size (n1) = 10 and n2 = 10 Pooled variance (sp2) = 180 Pooled…
Q: Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. H0:…
A: Given that Sample Variance 1 (s_1^2)(s12) = 10.710.7 Sample Size 1 (n_1)(n1) = 1515 Sample…
Q: The number of people in a car that crosses a certain bridge is a random variable x. The toll on the…
A: Given The random variable X denotes the number of people in a car The toll charges: $ 5 per car…
Q: A company is doing a hypothesis test on the variation in quality from two suppliers. Both…
A: Claim : the variance in quality for supplier 1 is larger than supplier 2.Formula UsedTest…
Q: The main number of English courses taken in a two-year time period by male and female college…
A: It is given that the experiment consists of 29 males and 16 females. Sample mean and standard…
Q: An ecologist is studying the impact of local polluted waters on the growth of alligators. The length…
A: Length of adult male alligators follows a normal distribution with µ and standard deviation 2. n…
Q: In drilling a vertical wellbore, the spacing between major fractures are recorded It has been found…
A: Standard normal distribution: The standard normal distribution is a special case of normal…
Q: An electronic company's records show that the mean number of circuit.boards rejected per batch is…
A: It is given that Sample size n = 10 Sample variance s2 = 2.5 Population variance = 1.4
Q: An experiment is assessing the effect of exercise regimen on cholesterol level decrease. A random…
A: n=45, population variance=σ2=20,X¯=30
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 28 images
- A maple syrup packager conducts some tests of the sugar content of their latest batch of canned maple syrup. A random sample of 10 cans of maple syrup yields a sample standard deviation of 4.8 milligrams. a) Test the claim that the variance equals 18 (milligrams)2 using the 5 percent level of significance. b) Find the p-value for this test.The University of Florida is interested in determining if there is a difference in the amount of money spent on food every two weeks between male and female students. They take a random sample of 20 male students (group 2) and 20 female students (group 1). They also find that xbar2 is 106 with a standard deviation of 14, and xbar1 is 146 with a standard deviation of 39. Do not assume equal variances. Find the test statistic for the difference in the amount of money spent. (Round your answer to one number after the decimal.)A paint manufacturer wants to introduce a new paint on the market. The following data were obtained for drying time (minutes) when five samples of the paint were tested. 380 290 240 310 300 Assuming that the drying time is normally distributed with a variance of 400, obtain a 99% confidence interval for the true mean drying time.
- A study tested the claim that heights of Americans and heights of Austrians have different variances with s=7.48092 cm for Americans and 7.14756 cm for Austrians. The sample sizes are n1= 145 and n2= 157. When using the F test with these data, is it correct to reason that there is no need to check for normalcy because n1 is greater than 30, and n2 is greater than 30?The data from an independent-measures research study produce a sample mean difference of 4 points, and each sample has a variance of 10. If there are n = 20 scores in each sample, then what is the estimated standard error of the difference between means?Gestation period is the length of pregnancy, or to be more precise, the interval between fertilization and birth. In Syrian hamsters, the average gestation period is 16 days. Suppose you have a sample of 31 Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups, and who have an average gestation length of 17.1 days and a sample variance of 26.0 days. You want to test the hypothesis that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is sMM= a. 31, b. 0.5232, c. 0.7328, d. 0.9158. The t statistic is- a. 1.50, b. 2.10, c. 2.63, d. 1.20 Now suppose you have a larger sample size n = 95. Calculate the estimated standard error and the t statistic for this sample with the same sample average and the same…
- A researcher is interested whether a new drug is effective in changing patients' cholesterol levels. She divided 33 patients into 3 groups according to the dosage the patient received. The cholesterol levels of all patients are measured and used as the data for the Analysis of Variance (ANOVA). If she reported the test statistic F = 2.1 What is the degree of freedom for the numerator of the F statistic? What is the degree of freedom for the denominator of the F statistic? What is the P-value of the F-test? (Round to 3 decimals) Given the significance level of 0.01, what can she conclude from the test? *The patients in differnt groups have simliar average cholesterial levels. The drug made no difference. *At least one group of patients have an average cholesterol level that is different from the other groups. The drug may have an effect.In the manufacture of steel rollers to fit an assembly, the external diameter is considered to be a random variable with mean equal to 23 mm and variance equal to 0.0036 cm2. 1.5 is supported standard deviations more than the mean and 3.5 standard deviations below average. A piece with a diameter below such specifications is considered waste, whereas a piece with a diameter larger than specified must be reprocessed. Which is the percentage of pieces that:to. They are being wasted.b. They need to be reprocessed.c. Acceptable.d. If you want to establish that the reprocessing is 5% of the rollers and waste of 1%, than specification limit would recommend.A psychologist has developed a standardized test for measuring vocabulary skill for 4 year old children. The scores on the test form a normal distribution with u = 70 and o = 20. A researcher would like to use the test to investigate the hypothesis that children who grow up as an only child develop vocabulary skills at a faster rate than children in larger families. A sample of n=25 only children is obtained and the mean test score for the sample is M = 77. Perform a two tailed hypothesis test, with an alpha level of .05, and add an APA summary.
- A researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale. Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.A two-sample study for the difference between two population means will utilize t-test procedures and is to be done at the 0.05 level of significance. The sample sizes are 23 and 27. The variances are 18 and 36, respectively. What is the upper critical value t, for the rejection region if:(a) the alternative hypothesis is one-sided, and you assume that the population variances are vunequal?(b) the alternative hypothesis is two-sided , and you assume that the population variances are unequal?(c) the alternative hypothesis is one-sided and you assume that the population variances are equal?(d) the alternative hypothesis is two-sided, and you assume that the population variances are equal?An HIV clinical trial with 1151 subjects was conducted. We will focus on two variables from this trial: IVDrug and Age. IVDrug is a categorical variable that indicates whether each subject never, previously, or currently uses IV drugs. Age lists the subject's age in year. Thus, we have age for subjects in three treatment groups. Assume that the samples were collected independently and come from a normally distributed population with equal variances. An ANOVA is used to test whether average age in the three IV drug groups is the same. A partially filled-in ANOVA table is listed below. Use a significance level of 0.05. p-value Treatment Error Total df SS MS 76.77 F 7.5586