9) A group of scientists study the breeding times of caterpillars who are fed a supplemented diet versus a control group that is fed a normal diet. Control Group n1 = 6 X1 = 4.00 days $1 = 3.11 days Supplemented Group n2 = 7 x2 = 11.30 days s2 = 3.93 days a) State the null and the alternative hypothesis for this comparison. b) Carry out a two sample t-test. c) What can you conclude?
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- 1) A cement producer, manufactures and then fills 40kg-bags of powder cement on twodistinct production tracks located in separate suburbs. To determine whether differencesexist between the average fill rates for the two tracks, a random sample of 25 bags fromTrack 1 and a random sample of 16 bags from Track 2 were recently selected. Each bag’sweight was measured and the following information measures from the samples arereported:Production ProductionTrack 1 Track 2n1 = 25 n2 = 16x2 = 40.02 x1 = 39.87 s1 = 0.59 s2 = 0.88 Supervision believes that the fill rates of the two tracks are normally distributed with equalvariances.Construct a 95% confidence interval estimate of the true mean difference between the twotracks.--------------------------------------------------------------------------------------------------------------2) Two independent simple random samples were selected from two normallydistributed populations with unequal variances yielded the following information:Sample 1…1. In the book Design and Analysis of Experiments, 8th edition (2012, John Wiley & Sons), the results of an experiment involving a storage battery used in the launching mechanism of a shoulder-fired ground-to-air missile were presented. Three material types can be used to make the battery plates. The objective is to design a battery that is relatively unaffected by the ambient temperature. The output response from the battery is effective life in hours. Three temperature levels are selected, and a factorial experiment with four replicates is run. The data are as follows: Table 11.(a) Test the appropriate hypotheses and draw conclusions using the analysis ether either firing temperature or furnace position affects the baked density of a carbon anode. The data are as follows: Table 12.(a) State the hypotheses of interest. (b) Test the hypotheses in part (a) using the analysis of variance with a = 0.05. What are your conclusions? (c) Analyze the residuals from this experiment. (d)…19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance. 19a. Step 2: Compute the df and locate the critical values. df = _______ Critical value = ________
- 19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance. 19. Step 1: Which of the following is the correct set of hypotheses?A. H0: The preferences will not match production (40% Half Pint, 40% XXX, 20% Dark Knight); and H1: The preferences will match production B. H0: \mu_{1}μ1 = \mu_{2}μ2 = \mu_{3}μ3; and H1: At least one of the categories will be different than the others C. H0: The preferences will match production (40% Half Pint, 40% XXX, 20% Dark Knight); and H1: The preferences will not match production 19b. Step 2: Compute the df and locate the…19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance. 19. Step 3: Compute the test statistic -- Chi-square χ2 = (use 2 decimal places) _____________ Step 4: Decision and Conclusions 19. Step 4: Decision: A. Reject H0 B. Retain H0 19. Step 5: Conclusion: Did the production of the premium lagers match consumer preferences? A. Yes. The observed frequencies did not differ from the expected frequencies. B. No. The observed frequencies differed from the expected frequencies.19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance.
- 1)Remove the four potential outliers of 0, 0, 8, and 20, and then obtain a new histogram without the outliers. Does the data appear to be normally distributed now? 2)Assuming that the four potential outliers of 0, 0, 8, and 20 are not recording errors, repeat the hypothesis test from part (c) (again setting up the hypothesis test and using either the critical value or p-value approach), and compare your results with that obtained in (c). Did you make a different conclusion? 3)Imagine you know have to make a recommendation/conclusion to the company that hired you: Assuming that the four potential outlies are not recording errors, and looking at the two results above, would you recommend using the first test with the outliers or the second test with the outliers removed? There is no right or wrong answer here, I am interested in what you think and your reasoning.31% of all pygmy softshell tortoises have stripes on their shells. A herpetologist in Cititon collects a sample of 28 pygmy softshell tortoises and finds that 8 of them have stripes on their shells. Is there enough evidence to conclude, at a significance of alpha = 0.05, that the proportion of pygmy softshell tortoises in Cititon with stripes on their shells is less than 31%? What is the claim? What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? What is/are the critical value(s)? Do we reject the null hypothesis? What conclusion do we draw? What is the P-value for the problem above?A study was performed on 200 elementary school students to investigate whether regular Vitamin A supplementation was effective in preventing colds during the month of March. 100 were randomized to receive daily Vitamin A supplements during the month of March, and 100 students were randomized to a placebo group (and did not receive Vitamin A) during the same month. The number of students getting at least one cold in March was computed in the two groups, and the results are given in the following 2 X 2 table. Using a 5% level of significance determine whether there is an association between Vitamin A supplementation and prevention of Common Cold ColdNo Cold Vitamin A1585100 Placebo2575100 40160200
- 31% of all pygmy softshell toises have stripes on their shells. A herpetologist in Cititon collects a sample of 28 pygmy softshell tortoises and finds that 8 of them have stripes on their shells. Is there enough evidence to conclude, at a significance of alpha=0.05, that the proportion of pygmy softshell tortoises in Cititon with stripes on their shells is less than 31%? What is the claim? What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? What is/are the critical value(s)? Do we reject the null hypothesis? What conclusion do we draw? What is the P-value for the problem above?In analyzing the consumption of cottage cheese by members of various occupational groups, the United Dairy Industry Association found that 326 of 837 professionals seldom or never ate cottage cheese, versus 220 of 489 white-collar workers and 522 of 1243 blue-collar workers (Sheet 53). Assuming independent samples, use the 0.03 level in testing the null hypothesis that the population proportions could be the same for the three occupational groups. Sheet 53 Group 1 Group 2 Group 3 Total seldom or never 326 220 522 1068 often 511 269 721 1501 Total 837 489 1243 2569 Select one: a) chi-square stat = 4.81, crit. value = 7.01, fail to reject H0, population proportions are not different b) p-value = 0.09, reject H0, population proportions are not different c) chi-square stat = 4.81, crit. value = 9.2, fail to reject H0, population proportions are not different d) p-value = 0.029, reject H0, population proportions differentThe contingency table shows the result of a random sample of students by Ziyi Zhang at PCC and the number of hours they spend investing on Robinhood and Acorns by age and gender. At alpha =0.05, can you conclude that age is related to gender when it comes to time spent investing on Robinhood and Acorns. GENDER 16-20yrs 21-30yrs 31-40yrs 41-50yrs 51-60yrs 61yrs or older Male 45 170 90 72 45 26 Female 9 30 21 17 10 5 What is the Chi-square test statistics and the decision for this question. The Test statistics is . Leave your answer in 3 decimal places. DECISION: We the null hypothesis.