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 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.
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 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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