x1 1 2 3 4 5 y1 3 7 5 11 14
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From the data below;
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y1 |
3 |
7 |
5 |
11 |
14 |
Ho: β1 = 0
Ha: β1 ≠ 0
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- A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.34. A dietician is asked to test this claim and finds that a random sample of 16 servings has a variance of 1.22. At α=0.05, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.Questions are added as a picture from another file since there didn't seem to be a way to type some characteristics into this text field. A classmate is interested in estimating the variance of the error term in Yi = β0 + β1Xi + ui. a.) found on atta b.) found on attachmentAssume that you have a sample of n, = 8, with the sample mean X, = 47, and a sample standard deviation of S, = 7, and you have an independent sample of n, = 7 from another population with a sample mean of X, = 37 and the sample standard deviation S, = 8. Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that u, > H2? Determine the hypotheses. Choose the correct answer below. O A. Ho: H1 SH2 H1: Hy> H2 O B. Ho: H1 =H2 H: H1 # H2 O D. Ho: H1 H2 O C. Ho: H1> H2 H1: H1 SH2
- In the accompanying table, x is the tensile force applied to a steel specimen in thousands of pounds, and y is the resulting elongation in thousandths of an inch: x| 1 2 3 4 5 6 y 14 33 40 63 76 85 a ) Construct a 95% confidence interval for B1, the elongation per thousand pounds of tensile stress. Find a 95% prediction interval for the elongation of a specimen with xo = 3.5 thousand pounds. Test the null hypothesis Bo = 0.75 against the alternative hypothesis Bo > 0.75 at the 0.1 level of significance.For the test of the null hypothesis Ho: u = 17.5 against the two-sided alternative H,: µ # 17.5, a random sample from a normal population with known standard deviation resulted to the observed value of the Z-statistic z, %3D = 1.68. What is the p-value (“observed significance level") of the test? Select one: a. 0.09295 b. 0.17254 c. 0.07236 d. none of the answersTests the claim that 1 # p2. Assume the samples are normally distributed, random and independent. of + o S1 =0.77 ; s2 = 0.82 E1 = 48.92 ; z2 = 48.94 n1 = 24; n2 = 31 a. Calculate the Standard Error s-, = (use 3 decimal places) (use 2 decimal places) b. Calculate the t-test statistic using the standard error from part a. t = c. What are the degrees of freedom? df %3! d. At a = 0.02, Use the distribution table to find the critical values for the rejection region t = ± (use 4 decimal places) e. What is your conclusion? O Fail to reject the null hypothesis and do not support the claim O Reject the alternative hypothesis and support the claim O Accept the null hypothesis and support the claim O Reject the null hypothesis and support the claim O Accept the alternative hypothesis and reject the claim
- Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. Net weights actually vary slightly from bag to bag and are Normally distributed with mean u. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised, so he intends to test the hypotheses Ho: μ = 14, Ha: μ < 14. To do this, he selects 16 bags of this brand at random and determines the net weight of each. He finds the sample mean to be x = 13.88 and the sample standard deviation to be s = 0.24. Suppose in a similar test of 16 bags of these tortilla chips the P-value is 0.001. Further suppose that a is chosen to be 0.001. In that case, we would conclude that: Othere is not significant evidence that the mean net weight of the bags of chips is less than the advertised 14 oz. O there is not significant evidence that the mean net weight of the bags of chips is not less than the advertised 14 oz. O there is significant evidence that the…Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(The NAEP considers that a national average of 283 is an acceptable performance. Using α = .05, run a two-tail t-test for one sample to test Ho: µ=283 for the 2019 scores. Report the t-obt, df, and p-values. Would you reject the null hypothesis that the 2019 scores come from a population with average 283? If this is the case, does it come from a population from larger or smaller average?Suppose that a group of researchers is planning to test a new weight loss supplement. They have selected a random sample of 50 people who are trying to lose weight and plan to measure the amount of weight lost after one month of using the supplement. Assume that the researchers know from prior experiments that the standard deviation of weight lost in one month, o, is 1.5 lb. To show that the supplement is effective, they plan to use a one-sample z-test of Ho: =0 lb against H1: µ > 0 lb, where u is the mean amount of weight lost in one month. They have also determined that, for a test with a significance level of 0.01, the power of the test is 0.8348 if the mean amount of weight lost is actually 0.7 lb. What is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.7 lb or more? Give your answer as a percentage, precise to two decimal places.We have specified the “tailedness” of a hypothesis test for a population mean with null hypothesis H0: μ = μ0. a. draw the ideal power curve. b. explain what your curve in part (a) portrays. left-tailedSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. 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