If this was 2 sample independent data, what assumption(s) would we need to check? 25 normally distributed data equal variances all nip, > 5 multinomial experiment all E > 5 What is the value of our test statistic? Round to 2 decimal places. Type your answer..... 26 What is the critical value for the rejection region if this was a less than alternative hypothesis at the 1% significance level? Round to 3 decimal places. Type your answer....
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- A large scale industry manufacturers unique items for sale in the local market.The sales manager claims that advertisement of the products improves sales. Asample of 15 advertised products generated mean revenue of kshs.1.4M witha standard error of Kshs. 0.5 M. The 14 non advertised products had a meanrevenue of Kshs. 1.0M with standard deviation of Kshs. 0.4 M.At level of significance α = 1.0%, formulate the relevant hypothesis and check if the manager’sclaim is legitimateA researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms. Full data set Carpeted Uncarpeted 7.5 14.9 9.4 5.1 10.6 4.2 9.2 12.7 9.9 13.3 9.3 4.2 6.9 11.1 7.5 12.5 Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the α=0.05 level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers. State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms. A. H0: μ1=μ2 H1: μ1>μ2 This is the correct answer. B. H0: μ1<μ2 H1: μ1>μ2 C. H0: μ1=μ2 H1: μ1≠μ2 D. H0: μ1=μ2 H1: μ1<μ2 Your answer is not correct. Determine the P-value for this hypothesis test. P-value=nothing…a Light bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 10 of its light bulbs resulted in the following lives in hours. 993 595 512 839 739 917 871 755 918 729. At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P value method of testing hypothesis
- Researchers recruited a sample of 40 female and 40 male heterosexual Caucasian undergraduate students from British universities for a study of the attractiveness of body types. Among adults, a body mass index (BMI, in kg/m2 ) value between 18.5 and 24.9is considered healthy, but attractiveness may not be entirely about health. Using a 3D computer avatar, participants built what they considered the ideal body of an adult of their own gender. The Minitab output for the mean ideal BMI of the women and of the men respectively is shown. From Barbie dolls to runway models, women in Western countries are exposed to unrealistically thin and arguably unhealthy body standards for their gender. Does the study provide evidence that young Caucasian women in British universities, on average, aim for an unhealthy ideal body type (corresponding to a BMI less than 18.5 )? test statistic,t = p-value =Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is an important characteristic. A random sample of 10 gears from supplier 1 results in x1 = 290 and s1 = 12, and another random sample of 16 gears from the second supplier results in x2 = 310 and s2 = 22. Do the data support the claim that the mean impact strength of gears from supplier 2 is at least 10 foot-pounds higher than that of supplier 1, find the tcalc value? Please report your answer upto 3 decimal places.The article “Dynamics of Insulin Action in Hypertension: Assessment from Minimal ModelInterpretation of Intravenous Glucose Tolerance Test Data” (R. Burattini, M. Morettini, etal., Med Biol Eng Comput, 2011:831–841) compared levels of an insulin sensitivity index SIin patients with high blood pressure and patients with normal blood pressure. Ten patientswith high blood pressure had a mean value of 3.4 with a standard deviation of 0.6, and eightpatients with normal blood pressure had a mean value of 7.9 with a standard deviation of0.6. Units are 10−5 · min−1 · pmol−1. Find a 98% confidence interval for the difference inmean levels between those with high blood pressure and those with normal blood pressure.
- Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. The paper “Bone Mass Is Recovered from Lactation to Postweaning in Adolescent Mothers with Low Calcium Intakes” (Amer. J. of Clinical Nutr., 2004:1322-1326) gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in postweaning period (P). (Let = true mean difference in TBBMC, postweaning minus lactation.) Subject 1 2 3 4 5 6 7 8 9 10 L 1928 2549 2825 1924 1628 2175 2114 2621 1843 2541 P 2126 2885 2895 1942 1750 2184 2164 2626 2006 2627 Does the data suggest that true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g? State and test the appropriate hypotheses using a significance level of .05. [Note: The appropriate normal probability plot shows some curvature but not enough to…Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. The paper “Bone Mass Is Recovered from Lactation to Postweaning in Adolescent Mothers with Low Calcium Intakes” (Amer. J. of Clinical Nutr., 2004: 1322–1326) gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in the postweaning period (P). SubjectL 1928 2549 2825 1924 1628 2175 2114 2621 1843 2541P 2126 2885 2895 1942 1750 2184 2164 2626 2006 2627 Does the data suggest that true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g? State and test the appropriate hypotheses using a significance level of .05.DBTI’s leadership is looking at a wide variety of sample-based statistics to determine whether itis safe to resume limited in-person learning. Their null hypothesis is that the rate of COVID-19infection is no decreasing. Which of the following is an example of a Type II error? (select one)a. Concluding that the rate of infection is dropping when it is not dropping.b. Concluding that the rate of infection is not dropping when it is dropping.c. Concluding that the sample is small and the data are skewed in a way that prohibits usfrom using a normal distribution or a t-distribution in our analysis.d. Concluding that the sample data are biased because only symptomatic infections tendto be reported, and other testing shows a significant number of asymptomaticinfections.
- Managers of an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by , in dollars) and the maximum temperature (denoted by , in degrees Fahrenheit) for each of fifteen randomly selected days during the past year are given below. These data are plotted in the scatter plot in Figure 1.The following results were obtained by regressing mean hourly wage in dollars (Y) on years of schooling (X). Dependent Variable: MEAN_WAGE Method: Least Squares Date: 02/15/15 Time: 11:11 Sample: 1 13 Included observations: 13 Variable Coefficient Std. Error t-Statistic Prob. C -0.014453 0.874624 -0.016525 0.9871 YEARS_SCHOOLING 0.724097 0.069581 10.40648 0.0000 R-squared 0.907791 Mean dependent var 8.674708 Adjusted R-squared 0.899409 S.D. dependent var 2.959706 S.E. of regression 0.938704 Akaike info criterion 2.852004 Sum squared resid 9.692810 Schwarz criterion 2.938920 Log likelihood -16.53803 Hannan-Quinn criter. 2.834139…An experiment was conducted to test whether students’ performance (above or below average) is independent of stress level as a result of pressure on time table for the term in Hwanhwan Senior High School. The table below gives a 3 × 2 contingency table of the sample. Above Average Average Below Average Total Stressed 135 250 285 670 Not Stressed 150 157 107 414 Total 285 407 392 1084 With the help of chi-square test statistics, determine whether students' performance for the selected term in the school is independent of their stressed level experienced from the time table at α = 0.05