103 d-e please 7.13 Topic 13: Inference for Two Means100. Once a month samples of sea level from Key West, FL in 2016 had a mean level of 0.113m andstandard deviation of 0.0492m. Ten years earlier, once a month samples of sea level in the samelocation had mean of 0.014m and standard deviation 0.0373m. Researchers wish to estimate thechange in mean sea level in Key West from 2006 to 2016 with 95% confidence.Year Jan Feb2006 0.010 0.1202016 0.0100.010 0.101Diff 0.000 0.019******Dec Mean SD0.104 0.133 0.04920.082 0.014 0.03730.0220.0990.0380125(a) Explain why this is considered paired data.(b) What is the point estimate for the average difference?(c) What is the standard error of the difference in means?(d) What is the margin of error?(e) Construct and interpret the confidence interval for the mean difference in sea level between2006 and 2016.101. Is sea level the same along all coastal regions? To examine this a sample of 12 coastal locationsin the Gulf Coast had mean sea level 5.3953m and standard deviation 2.2559m. A sample of 17locations along the eastern seaboard had mean 3.4028m and standard deviation 1.036m.(a) What is the point estimate for the difference in mean sea level?(b) What is the standard error of the difference in means?(c) What is the margin of error for a 99% confidence interval?(d) Construct and interpret the confidence interval for the difference in mean sea level betweenthe Gulf Coast and the eastern seaboard.(e) Based on the interval, do you expect there to be evidence or little to no evidence for Ha#1 #2? Explain without conducting the hypothesis test.102. Is there a difference in the average age that people get married in the US and its close neighbor,Canada? Suppose a random sample of 30 Americans had an average age of marriage of 28 yearswith standard deviation 3 years. For a random sample of 30 Canadians, the average age was 30.1years with standard deviation 3.3 years.(a) Construct a 95% confidence interval for the difference in average age of marriage betweenCanadians and Americans.(b) Interpret the interval.(c) Based on the interval alone, what would you conclusion be in a two-sided test of Ho1 - 2 = 0? Explain without conducting the test.103. In an interesting series of tests by Wilson et. al. in Science 2014, participants were asked to sitalone with their thoughts for 15 minutes. Participants were able to have either no stimulationduring this period or negative stimulation in the form of a self administered electric shock. The 18men in the sample elected to shock themselves an average of 1.47 times with standard deviation1.46 (not including one outlier who shocked himself 190 times). The 24 women in the studyshocked themselves an average of 1 time with standard deviation 2.32 times. It is interesting to 126note that these participants all said they would pay not to receive the shock in an earlier portionof the study! Is there significant evidence that men have a harder time sitting alone with theirthoughts (i.e administered more shocks) than women?(a) State the hypotheses for the test.(b) Calculate the test statistic.(c) Find and interpret the p-value.(d) State the conclusion of the test.(e) Based on the conclusion, do you expect a confidence interval to contain zero? Explainwithout constructing the interval.104. Referring back to the interesting series of tests by Wilson et. al. in Science 2014, participantswere asked to sit alone with their thoughts for 15 minutes. Researchers wondered if it was hardfor participants to sit alone with their thoughts because of the unfamiliar laboratory setting.Therefore, some subjects were allowed to complete the experiment at home. The 146 partici-pants completing the experiment in the lab had a mean "enjoyment score" of 5.12 with standarddeviation 1.77. The 44 participants completing the experiment from home had a mean "en-joyment score" of 4.35 with standard deviation 1.95. Is there significant evidence to concludethat environment (home vs. lab) caused a difference in mean enjoyment score? Perform theappropriate test.0000

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(a) State the hypotheses for the test. (b) Calculate the test statistic. (c) Find and interpret the p-value. (d) State the conclusion of the test. (e) Based on the conclusion, do you expect a confidence interval to contain zero? Explain without constructing the interval.