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- Is narcissism a more common personality trait today than it was a few decades ago? It is known that the mean population score on the Narcissistic Personality Inventory (NPI) for students attending University of South Alabama around 20 years ago was μ= 15 (Twenge, 2010). Interested in the narcissism levels of students in the year 2020, a researcher administers the NPI to a random sample of 25 University of Alabama sophomores this Spring term. The mean NPI score from the researcher’s sample of sophomores is M = 16.5, with s = 3.4. 1. Find the obtained (i.e., computed) test statistic for a sample (n=25) with a mean of 16.5 2. Make a statistical decision about the null. Will you reject or fail to reject the null based on your sample data? 3. Justify your decision about the null.An experiment was conducted on rodents to determine if the drug Haldol influenced the amount of "rough play." Five groups were included in the experiment. Subsequent behavior in terms of mean "rough play" behaviors was recorded. The output and box plot below, display the mean differences from baseline (i.e., after the drug was administered compared to before drug administration). What are the null and alternative hypotheses of this test? Summary of Roughplay differences Scd. Dev. Haldol dese Mean Freq. -.63158419 13.290618 19 Vehicle | 0.025 mg i 0.05 mg/ 1 0.1 mg/k -12.754389 13.783537 0.2 mg/k I 18 1.1481501 20.447041 5.0499951 16.035879 20 19 -20.S5 16.431064 20 Total -5.6631968 1B.558994 96 Analysis of Variance Frob F (p-value) Source SS df KS F Test- Statistic 8999.32832 4 2249.33203 9.63 0.0000 Between groups Within groups 91 260.682623 23722.1178 Tozal 32721.4461 95 344.436275 chif (4) 4.1710 Prob>chiz = 0.303 = Bartlett's test for equal variances: Roeghpiay diferences -50 Ho: 0…O CONFIDENCE INTERVALS AND HYPOTHESIS TESTING t distribution Use the ALEKS calculator to solve the following problems. (a) Consider a t distribution with 14 degrees of freedom. Compute P(-1.82Data are collected in an experiment designed to in- vestigate the impact of different positions of the mother during ultrasound on fetal heart rate. Fetal heart rate is measured by ultrasound in beats per minute. The study includes 20 women who are as- signed to one position and have the fetal heart rate measured in that position. Each woman is between 28 weeks and 32 weeks gestation. The data are shown in Table 7–7. Is there a significant difference in mean fetal heart rates by position? Run the test at a 5% level of significance. back side sitting standing 140 141 144 147 144 143 145 145 146 145 147 148 141 144 148 149 139 136 144 145A hypertensions trial is mounted and 12 participants are randomly assigned to receive either a new medication or a placebo. Each participant takes assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned medication the data are shown in table 7-9 is there a difference in the mean SBP between treatment? Run the appropriate test at a =0.05An occupational safety officer for a large company is conducting a study to investigate back problems in office workers who use a computer for most of the workday. The study will investigate the difference in back problems for workers who stand and workers who sit. A group of 68 volunteers have agreed to participate in the nine-month study. Half the group is randomly assigned to work while standing, and the other half is assigned to work while sitting. At the end of the study, the mean number of back problems between the two groups will be calculated. The officer will use the results to estimate the difference in the mean number of back problems between those who work while standing and those who work while sitting. Which of the following is an appropriate inference procedure for the study? A A one-sample t-interval for a population mean A one-sample t-interval for a sample mean A matched pairs t-interval for a mean difference D A two-sample t-interval for a difference between sample…A purchasing manager for a large university is investigating which brand of LCD projector to purchase to equip their classrooms. Of major concern is the longevity of the light bulbs used in the projectors. The purchasing manager has narrowed down the choice of projector to two brands, Infocus and Proxima, and wishes to determine if there is any difference between the two brands in the mean lifetime of the bulbs used. The purchasing manager obtained thirteen projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the thirteen projectors is given in the table. Lifetimes of light bulbs (hours) Infocus 830, 867, 1013, 986, 819, 809, 691, 903, 673, 909, 957, 820, 715 Proxima 532, 718, 769, 806, 779, 970, 903, 1043, 947, 792, 841, 752, 689 Send data to calc... v Send data to Excel Assume that the two populations of lifetimes, are normally distributed and that the population variances are equal. Can we conclude, at the 0.01…Why would the null hypothesis not be the mean lifespan of sexually inactive males (62.5)?A researchers says that 50% of the variance in blood pressure can be predicted from HR and that blood pressure is postively associated with HR. What is the correlation between blood pressure and HR?Is narcissism a more common personality trait today than it was a few decades ago? It is known that the mean population score on the Narcissistic Personality Inventory (NPI) for students attending University of South Alabama around 20 years ago was μ= 15 (Twenge, 2010). Interested in the narcissism levels of students in the year 2020, a researcher administers the NPI to a random sample of 25 University of Alabama sophomores this Spring term. The mean NPI score from the researcher’s sample of sophomores is M = 16.5, with s = 3.4. 1. Write the null and alternative hypotheses in symbols. Possible symbols for your answer: H0, H1, μ, M, σ. 2. Calculate the standard error. 3. Find the critical value for the test statistic, assuming alpha = .05 (Use largest [i.e., most conservative] value if exact value not given in the chart) a) 2.064 b) 1.96 c) 1.98 d) 2.000Liu et al. (2015) recently reported the results of a study examining whether happy people live longer. The study followed a large sample of British women, aged 50 to 69, over a 10-year period. At the beginning of the study, the women were asked several questions including how often they felt happy. After 10 years, roughly 4% of the women had died. The following table shows a frequency distribution similar to the results obtained in the study. Lived Died Within 10 Years Total Happy Most of the Time 382 18 400 Unhappy Most of the Time 194 6 200 Total 576 24 n = 600 Do the data indicate a significant relationship between living longer and being happy most of the time? Test with α = .05. (Round your answers to two decimal places for χ²-critical and χ².) χ²-critical = χ² = Conclusion: Fail to reject the null hypothesis. There is a relationship between living longer and being happy most of the time. Reject the null hypothesis. There is no relationship between living longer and being…Bone mineral density (BMD) is a measure of bone strength. Studies show that BMD declines after age 45. The impact of exercise may increase BMD. A random sample of 59 women between the ages of 41 and 45 with no major health problems were studied. The women were classified into one of two groups based upon their level of exercise activity: walking women and sedentary women. The 39 women who walked regularly had a mean BMD of 5.96 with a standard deviation of 1.22. The 20 women who are sedentary had a mean BMD of 4.41 with a standard deviation of 1.02. Which of the following inference procedures could be used to estimate the difference in the mean BMD for these two types of womenSEE MORE QUESTIONS