Using data below 2 3 4 13 19 Solid content [%] 01 Chemical oxygen demand [%) 0 5 11 a) Find 95% confidence intervals of both parameters. b) Perform a hypothesis test that the slope, by 1, as against the alternative that b₁ > 1 at 95% confidence level.
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- You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n=18,you determine that b1=4.6 and Sb1=1.9. c. Based on your answers to (a) and (b), what statistical decision should you make? d. Construct a 95% confidence interval estimate of the population slope, β1.A researcher developed a regression model to predict the cost of a meal based on the summated rating (sum of ratings for food, decor,and service) and the cost per meal for 12 restaurants. The results of the study show that b1=1.4379 and Sb1=0.1397. a. At the 0.05 level of significance, is there evidence of a linear relationship between the summated rating of a restaurant and the cost of a meal? b. Construct a 95% confidence interval estimate of the population slope, β1. a. Determine the hypotheses for the test. Choose the correct answer below. A. H0: β1=0 H1: β1≠0 B. H0: β0≤0 H1: β0>0 C. H0: β1≤0 H1: β1>0 D. H0: β0≥0 H1: β0<0 E. H0: β1≥0 H1: β1<0 F. H0: β0=0 H1: β0≠0 Compute the test statistic. The test statistic is ? (Round to two decimal places as needed.) Determine the critical value(s). The critical value(s) is(are) ? (Use a comma to separate answers as needed.…Test the null hypothesis that the slope is zero versus the two-sided alternative in the following setting using the alpha = 0.05 significance level: n = 100, yhat = 29.3 + 2.1x, and SEb1 = 1.05.
- In exercise 7, the data on y = annual sales ($1000s) for new customer accounts andx = number of years of experience for a sample of 10 salespersons provided the estimatedregression equation yˆ = 80 + 4x. For these data x = 7, o(xi − x)2 = 142, and s = 4.6098.a. Develop a 95% confidence interval for the mean annual sales for all salespersons withnine years of experience.b. The company is considering hiring Tom Smart, a salesperson with nine years of experience.Develop a 95% prediction interval of annual sales for Tom Smart.c. Discuss the differences in your answers to parts (a) and (b).Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C.I) = the width of the confidence interval for the average value y for a given value of x, and Width (P.I) = the width of the prediction interval for a single value y for a given value of x. Which of the following statements is true? Width (C.I) = 0.5 Width (P.I) Width (C.I) = Width (P.I) Width (C.I) > Width (P.I) Width (C.I) < Width (P.I)An urban community wants to show that the incidence of breast cancer is higher in their locality than in a neighboring rural area. (PCB levels were found to be higher in the soil of the urban community). If you find that in the urban community 20 out of 200 adult women have breast cancer and that in the rural community 10 out of 150 adult women have it, could you conclude, at a significance level of 0.05, that breast cancer is more prevalent in the urban community?1. The parameter of interest is:2. The hypotheses for this test are:3. The calculated test statistic is:4. The critical region is:5. Draw the critical region (make decision):6. It can be concluded that:
- 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?Assume that you have a sample of n1=8, with the sample mean x1=44, and a sample standard deviation of s1=5, and you have an independent sample of n2=14 from another population with a sample mean of x2=35, and the sample standard deviation s2=6. Construct a 95% confidence interval estimate of the population mean difference between m1 and m2. Assume the the two population variances are equal.A random sample of 12 hollyhock plants grown from the seed in a particular packet wastaken, and the height of each plant was measured, in m. The results are summarized by∑ ?ᵢ = 28.43, ∑ ?ᵢ² = 88.4704.Making a suitable assumption about the distribution of heights, which should be stated, find a90% confidence interval of the form of(?, ?), for the mean height of hollyhock plants grownfrom that packet.
- Based on the sample data set: (0,0) ( 2,3) (3,3) (6,4) (9,8) A. Construct the 90% confidence interval for the slope B1 of the population regression line B. find the Coefficient of determination using the formula r2=B1SSxy / SSyy.A nationwide study of undergraduate students reported that the mean number of drinks consumed per week during the spring semester is 7.96. The mean number of drinks consumed per week at USC is 7.64 (s.d.=2.55, N=412 Health services is concerned that USC students are consuming significantly more alcohol per week than the national average. Using an alpha level of .05, Is there sufficient evidence to be concerned? Be sure to select the correct critical value for the alternative hypothesis, and then use this evidence to make your conclusion1) A study of 29 female Sumatran elephants provided a 96% confidence t-interval for the mean shoulder height of all female Sumatran elephantsas (195.8, 235.4) cm. a) What is the reasonable point estimate for themean shoulder height of all female Sumatranelephants, µ.A. 195.8cm.B. 215.6cm.C. 235.4cm.D. All of the aboves are reasonable point estimates for µ.E. Since we don’t know the population, wecan’t estimate µ. b) Assume the margin of error is 10. Whatis the standard error (SE) of the mean?A. 4.642B. 4.651.C. 4.883.D. 4.890.E. Cannot calculate based on the given information.