Q1. Data were collected on the number of visitors of a shopping mall. The data are presented in the following table. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec No. of visitors 22 30 25 38 25 42 41 46 27 57 50 60 (a) Find the lag 2 autocorrelation coefficient ( r2) and interpret the result. (b) Develop a hypothesis test to determine whether the lag 2 autocorrelation coefficient is significantly different from zero.
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- A suburban hotel derives its revenue from its hotel and restaurant operations. Theowners are interested in the relationship between the number of rooms occupied on anightly basis and the revenue per day in the restaurant. Below is a sample of 25 days(Monday through Thursday) from last year showing the restaurant income and numberof rooms occupied.. A study is conducted on the relationship of the number of absences (x) and the grades (y) of 15 students in BC212. Using r at 0.05 level of significance and the hypothesis that there is no significant relationship between absences and grades of the students in BC212, determine the relationship using the following data.r.05 = - 0.514Number of Absencesx Grades in BC212y122338614551219 908580758065709580807592898065a. In the analysis of a scatterplot, the element/s that should be considereddirectionstrength of correlationboth direction and relationshipnone of theseb. The important numerical value in hypothesis testing isparametersample valueconclusioninterpretation
- In a clinical trial, 29 out of 853 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 2.9% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.9% of this drug's users experience flulike symptoms as a side effect at the α=0.1 What is the test statistic z0?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 = 0.05A researcher is concerned that his new antihypertensive medication may be causing insomnia in some of his patients. Suppose he gathers an SRS of 65 patients treated with the study drug with a sample average of 6.6 hours of sleep and a σ=1.1. Assuming that insomnia can be quantified as an average of 4.5 hours of sleep, can we determine with 95% confidence that his drug avoids diagnosis of insomnia as a side-effect?
- 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?A researcher is using a two-tailed hypothesis test with α = .05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample?Suppose a research study uses two independent groups with 21 individuals in each group. If a t-test analysis produces a calculated value of t of 1.68, which of the following is the correct decision?A. At the .05 level of significance, reject the null hypothesisB. At the .01 level of significance, reject the null hypothesisC. At the .05 level of significance, fail to reject the null hypothesisD. Impossible to answer without additional information
- A Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis. If μ1 and μ2 represent the mean depression score for male teens and female teens respectively, which of the following is an appropriate pair of hypotheses in this case? Check all that apply.A survey on lamb farms was conducted and data were collected on the followingvariables from a random sample of 30 farmers. Y = average live weight of ewes (kg)X1 = area of grazing land (m2) X2 = proportion of farm area that cannot be cultivatedX3 = proportion of area closed for lambs before weaningThe researchers reported:" A 2x2 ANOVA revealed, first of all, a main effect for depletion, indicating that depleted individuals generated less ideas (M = 9.40, SD = 5.64) than non-depleted individuals (M = 12.44, SD = 7.34), F (1, 108) = 6.03, p = .016, n2 = .05. This effect was qualified by the expected interaction with [perseverance], F (1,108) = 4.52, p = .036, n2 = .05". What size are the effects for the main effect of depletion and for the interaction between depletion and perseverance, according to Cohen's conventions? a. These are small- to -medium effects b. These are non existent effects c. These are large effects d. We are unable to tell from from the n2 / r2 statistics