An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 47 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) O Part (b) O Part (e) O Part (d) O Part (e) What is the test statistic? (If using the z distribution round your answers two decimal places, and if using thet distribution round your answers three decimal places.) t V =L O Part () What is the p-value? O p-value < 0.010 O 0.010 0.100 Explain what the p-value means for this problem. O If Ho is false, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more. O f H, is true, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more. O f Ho is true, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more. O ff Ho is false, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more.
An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 47 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) O Part (b) O Part (e) O Part (d) O Part (e) What is the test statistic? (If using the z distribution round your answers two decimal places, and if using thet distribution round your answers three decimal places.) t V =L O Part () What is the p-value? O p-value < 0.010 O 0.010 0.100 Explain what the p-value means for this problem. O If Ho is false, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more. O f H, is true, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more. O f Ho is true, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more. O ff Ho is false, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 47 students
and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?
Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
O Part (a)
+ Part (b)
+ Part (c)
+ Part (d)
O Part (e)
What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)
t
O Part (f)
What is the p-value?
O p-value < 0.010
O 0.010 < p-value < 0.050
O 0.050 < p-value < 0.100
O p-value > 0.100
Explain what the p-value means for this problem.
O If Ho is false, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more.
O If Ho is true, then there is a chance equal to the p-value that the average time needed to complete an undergraduate degree is 5.1 years or more.
O If Ho is true, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more.
O If Ho is false, then there is a chance equal to the p-value the average time needed to complete an undergraduate degree is not 5.1 years or more.
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