A group of transfer bound students wondered if they will spend the same mean amount on texts and supplies each year at their four-year university as they have at their community college. They conducted a random survey of 54 students at their community college and 66 students at their local four-year university. The sample means were $945 and $1015, respectively. The population standard deviations are known to be $257 and $89, 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 = four-year university. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part C: In words, state what your random variable Xc − Xu represents. Choose one below: Xc − Xu represent the difference in the average cost of textbooks at four year college universities and community colleges. Xc − Xu represents the average cost of textbooks. Xc − Xu represents the difference in the cost of textbooks at four year universities and community colleges. Xc − Xu represents the average difference in the cost of textbooks at four year universities and community colleges Part D: state the distribution to use for the test. (round your answers to two decimal places.) X ~ N (___,____) Part E: What is the test statistic? (if using the z distribution round your answer to three decimal places.) z or t = ____
A group of transfer bound students wondered if they will spend the same mean amount on texts and supplies each year at their four-year university as they have at their community college. They conducted a random survey of 54 students at their community college and 66 students at their local four-year university. The sample means were $945 and $1015, respectively. The population standard deviations are known to be $257 and $89, 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 = four-year university.
NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is
Part C: In words, state what your random variable Xc − Xu represents. Choose one below:
- Xc − Xu represent the difference in the average cost of textbooks at four year college universities and community colleges.
- Xc − Xu represents the average cost of textbooks.
- Xc − Xu represents the difference in the cost of textbooks at four year universities and community colleges.
- Xc − Xu represents the average difference in the cost of textbooks at four year universities and community colleges
Part D: state the distribution to use for the test. (round your answers to two decimal places.)
X ~ N (___,____)
Part E: What is the test statistic? (if using the z distribution round your answer to three decimal places.)
z or t = ____
Part F: What is the p-value? (round your answer to four decimal places)
Part I: Explain how you determined which distribution to use. Choose one below.
- The standard normal distribution will be used because the samples involve the difference in proportions.
- The t-distribution will be used because the samples are dependent.
- The t-distribution will be used because the samples are independent and the population standard deviation is not known.
- The standard normal distribution will be used because the samples are independent and the population standard deviation is known.
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