A group of transfer bound students wondered if they will spend the same mean amount on texts and supplies each year at their fourryear university as they have at their community college. They conducted a random survey of 54 students at their community college and 65 students at their local four-year university. The sample means were $947 and $1012, respectively. The population standard deviations are known to be $254 and $87, respectively. Conduct a hypothesis test at the 5% level to determine if the means are statistically the same Let subscript c = community college and u = foursyear university. NOTE: If you are using a Student's t-dlstrlbution for the problem, including for paired data, you may assume that the underlying population is normally distributed, (In general, you must first prove that assumptlon, though.) El P=(=i state the null hypothesis 0 H0442) ltu 0 Ha team 0 Ha uc= Ma 0 Ho ue= Mu El Pan (b) State the alternative hypothesis 0 Ha ue= #v 0 Ha up = Mu 0 Ha I'd) ltu 0 Ha l'c 70 a X, represents the average ditrerence in the cost or textbooks at foureyear universities and community colleges 0 >70 a )7\" represents the ditrerence in the average cost otlextbooks at foureyear universities and community colleges El PM (6) State the distribution to use tor the test. (Round your answers to two decimal places.) x ( . i) El Pink) What is lhe test Stallstlc\" (If using the z dislribution round your answer to two decimal places, and it using the ldislnbution round your answer to three decimal places ) ---Select-- v = EIPIHU) What is the prvalue'? (Round your answer to tour decimal places ) Explain what the p-value means tor this problem 0 It Hg is true. then there Is a chance equal to the pvalue that the ditlerence between the sample average amount spent on texts and supplies each year at the tour-year university and the community college is -$65 to 865 0 It H0 is ialse, then there is a chance equal to the p-value that the sample average amount spent on texts and supplies each year at the four-year university is at least $65 less than or $65 more than the sampie average amount spent atthe community college 0 It HD IS false, then there Is a chance equal to the p-value that the dlerence between the sample average amount spent on texts and supplies each year at the four-year university and the community college Is ~$55 to $55 0 ll H.) is true, then there is a chance equal to the ovalue that the sample average amount spent on texts and supplies each year at the foureyear university is at least $65 less than or $65 more than the sample average amount spent at the community college El PM (a) Sketch a picture or this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-vaiue l/zrpsvalue) llztpevnlue) pvalue l/thvalue) llztpvalue) p-value O O ElPIOI) Indicate the correct decrsron ("reiect" or "do not reiect" the null hypothesis), the reason for it, and write an appropriate conclusion (i)AIpha (Enter an exact number as an integer, traction. or decimal ) a (ii) Decision 0 reiect the null hypothesis 0 do not reject the null hypothesis (ill) Reason for decision 0 Since the p-value > t1, we reject the null hypomesis, 0 Since the p-value > tz. we do not reject the null hypothesis. 0 Since the p-value