(Solved): A study is done to determine if students in the California state university s ...

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A study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are \( 1.5421 \) years and 1 year, respectively. The following data are collected. The California state university system students took on average \( 4.5 \) years with a standard deviation of \( 0.9 \). The private university students took on average \( 4.1 \) years with a standard deviation of \( 0.2 \). Conduct a hypothesis test at the \( 5 \% \) level. 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.) State the distribution to use for the test. (Round your answers to two decimal places.) \[ \bar{X}_{\text {state }}-\bar{X}_{\text {private }} \sim(\quad, \quad) \] Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the \( t \) distribution round your answer to three decimal places.) \[ = \] Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the \( \rho \)-value means for this problem. graduation time of students at private universities. graduation time of students at private universities. time of students at private universities. graduation time of students at private universities. Correctl A p-value is the probability that an outeome of the data will happen purely by chance when \( H_{0} \) is true. Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the \( \rho \)-value. (Upload your file below.) No file chosen This answer has not been graded yet.