Question 1 (5 marks): A 2016 study reported in Science magazine stated that college math teachers scored a mean of 3.4 points for providing feedback to students on their work. Assume the sample size was 26 and the sample standard deviation was 1.5. Give the best point estimate for the population and construct a 99% confidence interval for the true population mean, stating the null and alternative hypothesis. Question 2 (5 marks): According to Facebook, the mean number of community pages, groups and events that users are connected to is 80. A random sample of 64 Facebook users showed a mean of 86 connections to community pages, groups, and events. The sample standard deviation is 48. Test at a 5% significance whether the population mean number of connections to community pages, groups and events is greater than 80, stating the null and alternative hypothesis Question 3 (5 marks): Below are the summary statistics for female verses male body temperatures in Fahrenheit Gender Sample Size Sample mean Sample standard body deviation temperature Females 27 98.394 0.743 Males 13 98.015 0.699 Using a 5% significance test the hypothesis that female body temperature is the same as male body temperature.Questions 4 (5 marks): The following data shows students marks before and after they attended a remedial statistic \"boot camp\". Is there evidence at the 0.05 level of signicance that the boot camp improved the participants' scores on the statistics test, stating the null and alternative hypothesis? Beforahnr Student mark mark D\" 1 1B 22 4 2 21 25 4 3 16 17 1 4 22 24 2 5 19 16 -3 B 24 29 5 7 17 2O 3 8 21 23 2 9 23 19 -4 10 1B 20 2 11 14 15 1 12 16 15 -1 13 16 18 2 14 19 26 7 15 1B 18 0 1B 20 24 4 17 12 18 5 1B 22 25 3 19 15 19 4 20 1? 16 -1 Mean 18.40 20.45 2.05 Questions 5 (5 marks): In 2010 the Pew Research Center reported that teenagers send on average 50 text messages every day. A researcher suspects this number is out of date, and wishes to determine if teens are sending fewer texts than they used to. A random sample of 25 teens were found to be sending an average of 47.75 texts per day, with a standard deviation of 15. Testing at 10% signicance and stating the null and alternative hypothesis, what can the researcher conclude