A manufacturer of television sets is interested in the effect of four different types of coating on tube conductivity for colour picture tubes. The following conductivity data are obtained. Assume that all assumptions to perform an ANOVA test are satisfied. Coating Type Conductivity 141 150 143 146 2 152 149 137 143 3 134 136 132 127 129 127 132 129 a) Perform an analysis to determine whether there is a difference in conductivity due to coating type? Use a = 0.05.
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Applied Statistical Methods
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- A clinical study was conducted on a medicine and the data obtained as follows: calculate Sensitivity Diseased •True Positive: 1000 •True negative: 50 Non diseased •True positive: 100 •True negative: 800The yield of alfalfa from a random sample of six test plots is 1.4, 1.6, 0.9, 1.9, 2.2,and 1.2 tons per acre. Assume the data can be looked upon as a sample from anormal population. Test at the 0.05 level of significance whether this supports thecontention that the average yield for this kind of alfalfa is 1.5 tones per acre.A manufacturer of television sets is interested in the effect on tube conductivity of four different types of coating for colour picture tubes. The following conductivity data are obtained. Assume that all assumptions to perform an ANOVA test are satisfied. Coating Type Conductivity 141 149 1 143 150 146 2 152 137 143 3 134 136 132 127 4 129 127 132 129 (a) Is there a difference in conductivity due to coating type? Use a = 0.05. (b) (c) Compute a 95% interval estimate of the mean of coating type 4. Compute a 99% interval estimate of the mean difference between coating types 1 and 4. (d) (e) Test all pairs of means using Duncan's multiple range test. Use a = 0.05. Assuming that coating type 4 is currently in use, what are your recommendations to the manufacturer? We wish to minimize conductivity.
- The manufacturer of a new eye cream claims that the cream reduces the appearance of fine lines and wrinkles after just 1414 days of application. To test the claim, 1010 women are randomly selected to participate in a study. The number of fine lines and wrinkles that are visible around each participant’s eyes is recorded before and after the 1414 days of treatment. The following table displays the results. Test the claim at the 0.050.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let women before the treatment be Population 1 and let women after the treatment be Population 2. Number of Fine Lines and Wrinkles Before 12 11 10 14 12 9 12 14 9 12 After 13 8 6 14 11 6 13 11 5 11 Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.An experiment was conducted to determine the effect of machining factors on ceramicstrength. Two levels of table speed (slow and fast), two directions (longitudinal and transverse) and two levelsof wheel grit (I and II) were identified by the researcher. The experiment was replicated three times and thestrength of each randomly selected ceramic was obtained. The ANOVA table of the results of the analysis areas follows. 1. Refer to the ANOVA table at a=0.01, what is the conclusion for testing significance in 3-way interaction Reject/Fail to Reject Ho 2. If sequential test of hypothesis is performed the following are (True or False)? a. All 2-way interaction effects are going to be tested b. All main effects are going to be tested 3. What combination of effects will result to a significant result at a=0.01 if should all test are going to be performed among the main effects and two way interactions? (choose 1pair/combination: direction, wheel grit, speed)Five samples of a ferrous-type substance were used to determine if there is a difference between a laboratory chemical analysis and an X-ray fluorescence analysis of the iron content. Each sample was split into two subsamples and the two types of analysis were applied, with the accompanying results. Assuming that the populations are normal, test at the 0.05 level of significance whether the two methods of analysis give, on the average, the same result. Determine the test statistic t=?
- Rhino viruses typically cause common colds. In a test of the effoctivoness of echinecea, 32 of the 39 subjects treated with echinacea developed ithinavirus infections In a placebo group, 90 of the 107 subjects developed thinovirus infections Use a 0.05 significance level to test the clam that echinacea has an effect on thinovinus infections Complete parts (a) through (c) below COO a. Test the claim using a hypothesis test Consider the first sample to be the sample of subjects treated with echinacea and the second samplo to be the sample of subjects troated with a placebo What are the null and alternative hypotheses for the hypothesis test? OA Ho P P2 H P P2 OB. Ho P P2 H P, P2 H, P Pa VE Ho Pr"P2 Hy P,P OF M PPa H, P P |OD. Ho P1 P2 H, P P2 Identify the test statistic (Round to two decimal places as noeded)Food deserts have become a particularly hot topic in the public health community as anexplanation for a variety of negative health outcomes in disadvantaged areas. Aresearcher is interested in comparing the average shelf space provided by supermarkets,convenience stores, and corner stores in two different communities in order to address thegrowing concern for food deserts. Assume the following table reports the summary statistics for shelf space dedicated to fresh fruits and vegetables (meters) obtained from SRSs of a variety of different stores that supply groceries from each community. Community Average Shelf Space For Fruits and Veg. (m) Sample Standard Deviation Sample Size "Food Desert" 13.7 2.4 12 Other Community 89.4 14.6 14 a) Carry out the appropriate statistical test in order to determine if there is a significant difference in mean shelf space between the two communities at the alpha level of 0.05. Assume all conditions for the test are met. Do not assume equal…A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters. Mean width: 7.555 Stdev width: 0.914 Mean height: 12.686 Stdev height: 1.634 Correlation coefficient: 0.8203 d) If the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation. e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.
- Use the Dunnett’s test to make comparisons among the three lubricating oilsto determine specifically which oils differ in brake-specific fuel consumptionat a 0.05 level of significance. Let lubrication oil 1 is the control.A pharmaceutical company is running a test comparing two forms of advertising for the same product one which involved a television campaign and the other a print campaign. Market sectors are randomly assigned to receive a particular form of advertising and product sales are recorded during the month following ad campaigns. Using the data provided test if there is a significant difference in product sales by method of advertisement. Use (alpha) a=0.05Prior to assessment of the outcome, the researchers did a manipulation check. Members of Groups 1 and 2 rated the attractiveness (on a 1 to 9 scale, with 9 being the most attractive) of the person in the photo. They reported that for the attractive photo, M = 7.53; for the unattractive photo, M = 3.20, F (1, 108) = 184.29. Was this difference statistically significant (using = .05 )? The p value F(1,108) = 184.29 is less than 0.0001. Therefore, the difference is statistically significant because the p value is much less than .05 What was the effect size for the difference in (2a)?