Data Collection: One-Sample Tests 1-B Instructions: Use the Interactive tool as directed to answer the questions below. DATA Sampling Cost = 800 Download CSV SETTINGS Reset Data Set Market Research Data Sample Size, n (2 - 200) 100 1-5 of 100 Rows > Sample Now No. Age RateNew RateCurr CurrBrand 1 45 3.1 7.1 B 2 24 8.6 6.5 A 3 28 1.5 6.5 C 4 32 3.3 9.9 A 5 41 8 3.8 A Use the dropdown menu to choose the Market Research Data data set. The variable descriptions are as follows: No.: An arbitrary Identification number assigned to each consumer surveyed Age: The age of the survey respondent RateNew: The respondent's rating of the new cell phone RateCurr: The respondent's rating of their current cell phone CurrBrand: The brand of the respondent's current cell phone Choose a sample of 100 observations. For the following question or analysis request, Identify the appropriate hypothesis test to perform. "The marketing efforts we will use will target consumers with an average age of 30. Is this sample representative of our target audicence with respect to age?" a. Conduct a (Click to select) with a hypothesized value of (Enter 999 if no test is needed.) b. The test or other calculations will use the following variable(s). (Mark variables used directly in calculating means, proportions, or a regression. Use existing variables whenever possible. Do not mark variables used only for sorting.) ? Age RateNew ? RateCurr ? CurrBrand ? A combination modification of one or more existing variables c. The test or calculations will use data from (Click to select) of the 100 observations.
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Perform and Interpret a One-Sample t Test (14 points total) The average MMSE score is around 25 in the general population aged 75 and up. The group of participants in our dataset have no neurological disorders and are well-educated. The researchers hypothesize that the population aged 75 or older would score significantly higher than the general population in the same age range. To conduct a one-sample t test manually, follow the steps below: 1. Create directional alternative hypothesis and null hypothesis from the research question "Do people aged 75 and up (µ1) targeted by this study score significantly higher on MMSE compared to the general population aged 75 and up (µ2= 25)?" Type the hypotheses out both in words and in symbol notations. (2 points: 1 for each hypothesis. If symbol notation or written format is missing for a hypothesis, deduct 0.5) 2. Conduct a one-tailed hypothesis test, with α = 0.05. Identify the critical t value from the t table. (1 point) 3. Calculate the t statistic by following the steps below: a. Calculate the sample mean, M. (1 point, must show manual calculation process to earn the point) b. Calculate the estimated population standard deviation s. (1 point, must show manual calculation process to earn the point) c. Calculate the standard error of the comparison distribution, sM. (1 point, must show manual calculation process to earn the point) d. Calculate the t statistic using the results from 3a, 3b, and 3c. (1 point, must show manual calculation process to earn the point) 4. Compare the t statistic with the critical t value to make a decision on the hypothesis test. - Is the t statistic more extreme than the critical t value? - Do you reject the null hypothesis? (2 points, 1 for each question) 5. Answer the research question based on the hypothesis test result. (1 point) 6. Calculate the standardized effect size of this hypothesis test. (1 point, must show manual calculation process to earn the point) 7. Copy and paste the 10 data points into SPSS and then run the one-sample t test in SPSS. Use the SPSS output to check your answers in the previous questions. Correct any errors and then report the t test result in symbols according to the APA standards, including t statistic with degree of freedom, p value, and effect size d. Present all the items in one single line separated by commas. Must paste the main t test result table (containing the p value) from SPSS output to earn the points. MMSE Age 29 76.9 29 79.9 28 84.1 30 75.6 28 79.6 26 78.0 28 78.9 28 78.4 29 76.8 28 76.5
Dominador T.
In a study conducted to investigate browsing activity by shoppers, each shopper was initially classified as a non-browser, light browser, or heavy browser. For each shopper, the study obtained a measure to determine how comfortable the shopper was in a store. Higher scores indicated greater comfort. The data collected are contained in the file Browsing.xlsx. Use a significance level α=0.05α=0.05 to test for differences among mean comfort levels for the three types of browsers. Hint: Refer to Sections 13.2 and 13.3 to help answer this question. (1) State the hypotheses. (2) Use XLSTAT to compute the F test statistic and the p-value. Hint: Select Modeling data > ANOVA. Select cells B1:B25 for “Y / Dependent variables: Quantitative” and select cells A1:A25 for “X / Explanatory variables: Qualitative.” The F test statistic and the p-value are in the last two columns of the Analysis of variance table in the XLSTAT output. (2) What is your hypothesis test decision? Hint: There are two possible decisions: reject H0 in favour of Ha or fail to reject H0. (2) What is your conclusion in the context of the application? Hint: The conclusion should relate back to the question. (4) If the conclusion in part (d) is that the population means are not all equal, use Fisher’s Least Significant Difference (LSD) Procedure to determine which pairs of browser types differ in terms of comfort. Hint: Calculate the sample means for each browser type and the absolute pairwise differences between the means. Then, calculate Fisher’s LSD critical value using the formula LSD=tα/2MSE(1ni+1nj)−−−−−−−−−−−−−√LSD=tα/2MSE(1ni+1nj) , where tα/2tα/2 is a critical value from a t-distribution with nT−k=24−3=21nT−k=24−3=21 degrees of freedom, MSE can be found in the Analysis of variance table in the XLSTAT output, and ni=nj=8ni=nj=8 . Then, see if any of the absolute pairwise differences between the means exceeds the calculated value of LSD. (4) Suppose we are not willing to assume that the populations have a normal distribution with the same standard deviations. Then, we should not use a parametric analysis of variance F-test, but we can instead use a nonparametric Kruskal-Wallis test for differences among median comfort levels for the three types of browsers. Use XLSTAT to compute the H test statistic and the p-value. Is the p-value similar to the corresponding value you obtained in part (b)? Hint: Select Nonparametric tests > Comparison of k samples (Kruskal-Wallis, Friedman, …). Make sure “One column per variable” is checked, select cells B1:B25 for Data, select cells A1:A25 for Sample identifiers, and select “Kruskal-Wallis test.” Under “Options” make sure “Asymptotic p-value” is selected. The H test statistic is labelled “K (Observed value)” in the XLSTAT output.
Aishwarya K.
a. Sample selection bias: a. Is only important for finite sample results b. Occurs when a selection process influences the availability of data and that process is related to the dependent variable c. Results in the OLS estimator being biased, although it is still consistent d. Is more important for non-linear least squares estimation than for OLS 2. Which of the following problems will not cause the endogeneity problem in a linear regression model? a. Omitting relevant variables b. Including irrelevant variables c. Errors in variables d. Simultaneous equations 3. The following is not a threat to external validity a. The treatment being studied is not representative of the treatment that would be implemented more broadly b. Experimental participants are volunteers c. The experimental sample is not representative of the population of interest d. Partial compliance with the treatment protocol 4. The conditions for valid instruments do not include the following: a. Perfect multicollinearity between the predicted endogenous variables and the exogenous variables must be ruled out b. Each one of the instrumental variables must be normally distributed c. Each instrument must be uncorrelated with the error term d. At least one of the instruments must enter the population regression of X and the Z's and the W's. 5. A study based on the OLS regressions is internally valid if: a. The errors are homoscedastic, and there are no more than two binary variables present among the regressors b. You use a two-sided alternative hypothesis and standard errors are calculated using the heteroskedasticity robust formula c. Weighted least squares produces similar results and the t-statistics is normally distributed in large samples d. The OLS estimator is unbiased and consistent and the standard errors are computed in a way that makes the confidence intervals have the desired confidence level 6. The following will not cause a correlation between X and u in the simple regression model: a. Irrelevance of the regressor b. Simultaneous causality c. Omitted variables d. Errors in variables 7. The distinction between endogenous and exogenous variables is a. Dependent on the distribution of the variables, i.e., when they are normally distributed, they are exogenous, otherwise, they are endogenous. b. Whether or not the variables are correlated with the error term c. That exogenous variables are determined inside the model and endogenous variables are determined outside of the model d. Dependent on the sample size, i.e., for n sufficiently large, endogenous variables become exogenous 8. The reliability of a study using a multiple regression analysis depends on all of the following with the exception of: a. Omitted variable bias b. External validity c. Presence of homoskedasticity in the error term d. Errors in variables
Sri K.
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