(i) Construct a 95% confidence interval of the difference in mean for the two solutions (ii) At the 5% significance level, test the null hypothesis that the difference between the mean etch rates of solution A and solution B is 0.1.
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- If the coefficient B₁ has a nonzero value, then it is helpful in predicting the value of the response variable. If B₁ = 0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that B₁ = 0 use the test statistic t = (b₁-0) /sp. Critical values or P-values can be found using the t distribution with n - (k+1) degrees of freedom, where k is the number of predictor (x) variables and n is the number of observations in the sample. The standard error sp, is often provided by software. For example, see the accompanying technology display, which shows that sp=0.076885101 (found in the column with the heading of "Std. Err." and the row corresponding to the first predictor variable of height). Use the technology display to test the claim that B₁ = 0. Also test the claim that B₂ = 0. What do the results imply about the regression equation? Click the icon to view the technology output. Test the claim that B₁ = 0. For…The output table below represents the results of the estimation of household expenditures (Y) and income (X) in thousand dollars. Considering the output table below, answer the following question. Dependent Variable: Y Method: Least Squares Date: 12/28/16 Time: 15:29 Sample: 2000 2010 Included observations: 11 a) Write the regressed equation and interpret the slope and the intercept. b) Construct a confidence interval for the slope (b2) at 95% confidence level. c) Test whether the slope is equal or not equal to zero at 95% confidence level.Women athletes at a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 23 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 10% level of significance. What is the level of significance? (b) State the null and alternate hypotheses. H0: p = 0.67; H1: p > 0.67 H0: p = 0.67; H1: p ≠ 0.67 H0: p < 0.67; H1: p = 0.67 H0: p = 0.67; H1: p < 0.67 What sampling distribution will you use? The Student's t, since np < 5 and nq < 5. The standard normal, since np < 5 and nq < 5. The standard normal, since np > 5 and nq > 5. The Student's t, since np > 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) Find the P-value of the test statistic. (Round your answer to four decimal places.)…
- 2. In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether there is no significant difference between the two means using a two - tailed with a = 0.01.(d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.) and (e) At the 0.10 level, can the owner conclude that the mean daily sales of the two stores differ? Yes NoA 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.
- (b) For a one-tailed test using the t-distribution, if the sample size is 20, find out the critical values based on the given significance levels: (1) a = 0.1, (2) a = 0.05, and (3) a = 0.01.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?A manufacturer of a new medication on the market for Parkinson's disease makes a claim that the medication is effective in 75% of people who have the disease. One hundred fifty individuals with Parkinson's disease are given the medication, and 100 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 75% claim the company made? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.
- Measurements of the sodium content in samples of two brands of chocolate yielded the following results: Brand A- n= 9, s = 2.642 , Brand B- n 13, s = 6.409 . Can you conclude, at the 1% significance level, that the sodium content is more variable in Brand B ? (Assume that sodium content is normally distributed.) (A) Yes (B) NoFrom this question I have to determine 1) what the independent and dependent variables are 2) state the estimated regression equation (in terms of the problem) using the given output. 3) what the interpretation for the slope of the regression line is 4) using the regression equation, predict the sales for a store with 3.4 million customers in it. Is this extrapolation or interpolation? 5) if I were to compute the 99% confidence interval for the slope of the regression line, what would the t critical value be? 6) the 99% confidence interval for the slope of the regression line in the above problem is? 7) assume that the number of customers increases by 2 million. What will be the range of values for the average increase in annual sales of the store? You may use the confidence interval from above to answer 8) is the corrrelation between number of customers and sales positive or negative? Why? 9) if the sales for a store with 2.2 million customers on it is 3.5 thousand dollars, what…
