Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) α = (ii) Decision: O reject the null hypothesis do not reject the null hypothesis (iii) Reason for decision: Since p-value>a, we do not reject the null hypothesis. Since p-value>a, we reject the null hypothesis. Since p-value Ha state private Part (c) In words, state what your random variable X state -X private represents. OX state-X private represents the average amount of time needed to graduate from a university. ○ X state - private represents the difference in the amount of time needed to graduate from a state university and a private university. ○ X state-X private represents the difference in the average amount of time needed to graduate from a state university and a private university. OX state-X private represents the average of the differences in the amount of time needed to graduate from a state university and a private university. Part (d) State the distribution to use for the test. (Round your answers to two decimal places.) X state-X private ? ✓ 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.) --Select-- = Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If Ho is true, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is at least 0.40 years more than the sample average graduation time of students at private universities. ○ If Ho is true, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is 0.40 or more years less than the sample average graduation time of students at private universities. If Ho is false, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is 0.40 or more years less than the sample average graduation time of students at private universities. If Ho is false, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is at least 0.40 years more than the sample average graduation time of students at private universities. Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. (Upload your file below.) Choose File No file chosen

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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please solve this problem step by step with clear explanation 

Part (h)
Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =
(ii) Decision:
O reject the null hypothesis
do not reject the null hypothesis
(iii) Reason for decision:
Since p-value>a, we do not reject the null hypothesis.
Since p-value>a, we reject the null hypothesis.
Since p-value <x, we reject the null hypothesis.
Since p-value <a, we do not reject the null hypothesis.
(iv) Conclusion:
There is sufficient evidence to conclude that the average time it takes for students to graduate from private universities is less than the time it takes for students to graduate from the California state university system.
○ There is not sufficient evidence to conclude that the average time it takes for students to graduate from private universities is less than the time it takes for students to graduate from the California state university system.
Part (i)
Explain how you determined which distribution to use.
○ The t-distribution will be used because the samples are independent and the population standard deviation is not known.
The t-distribution will be used because the samples are dependent.
The standard normal distribution will be used because the samples are independent and the population standard deviation is known.
The standard normal distribution will be used because the samples involve the difference in proportions.
Transcribed Image Text:Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) α = (ii) Decision: O reject the null hypothesis do not reject the null hypothesis (iii) Reason for decision: Since p-value>a, we do not reject the null hypothesis. Since p-value>a, we reject the null hypothesis. Since p-value <x, we reject the null hypothesis. Since p-value <a, we do not reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to conclude that the average time it takes for students to graduate from private universities is less than the time it takes for students to graduate from the California state university system. ○ There is not sufficient evidence to conclude that the average time it takes for students to graduate from private universities is less than the time it takes for students to graduate from the California state university system. Part (i) Explain how you determined which distribution to use. ○ The t-distribution will be used because the samples are independent and the population standard deviation is not known. The t-distribution will be used because the samples are dependent. The standard normal distribution will be used because the samples are independent and the population standard deviation is known. The standard normal distribution will be used because the samples involve the difference in proportions.
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 1.5841 years and 1 year, respectively. The following data are collected. The
California state university system students took on average 4.6 years with a standard deviation of 0.7. The private university students took on average 4.2 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.)
Part (a)
State the null hypothesis.
O Ho: state private
Ho state private
O Ho: state
private
O Ho state private
Part (b)
State the alternative hypothesis.
Ha state private
O Ha: state
private
O Ha state private
>
Ha state private
Part (c)
In words, state what your random variable X state -X private represents.
OX state-X private represents the average amount of time needed to graduate from a university.
○ X state - private represents the difference in the amount of time needed to graduate from a state university and a private university.
○ X state-X private represents the difference in the average amount of time needed to graduate from a state university and a private university.
OX state-X private represents the average of the differences in the amount of time needed to graduate from a state university and a private university.
Part (d)
State the distribution to use for the test. (Round your answers to two decimal places.)
X state-X private ? ✓
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.)
--Select-- =
Part (f)
What is the p-value? (Round your answer to four decimal places.)
Explain what the p-value means for this problem.
If Ho is true, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is at least 0.40 years more than the sample average graduation time of students at private
universities.
○ If Ho is true, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is 0.40 or more years less than the sample average graduation time of students at private
universities.
If Ho is false, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is 0.40 or more years less than the sample average graduation time of students at private
universities.
If Ho is false, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is at least 0.40 years more than the sample average graduation time of students at private
universities.
Part (g)
Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. (Upload your file below.)
Choose File No file chosen
Transcribed Image Text: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 1.5841 years and 1 year, respectively. The following data are collected. The California state university system students took on average 4.6 years with a standard deviation of 0.7. The private university students took on average 4.2 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.) Part (a) State the null hypothesis. O Ho: state private Ho state private O Ho: state private O Ho state private Part (b) State the alternative hypothesis. Ha state private O Ha: state private O Ha state private > Ha state private Part (c) In words, state what your random variable X state -X private represents. OX state-X private represents the average amount of time needed to graduate from a university. ○ X state - private represents the difference in the amount of time needed to graduate from a state university and a private university. ○ X state-X private represents the difference in the average amount of time needed to graduate from a state university and a private university. OX state-X private represents the average of the differences in the amount of time needed to graduate from a state university and a private university. Part (d) State the distribution to use for the test. (Round your answers to two decimal places.) X state-X private ? ✓ 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.) --Select-- = Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If Ho is true, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is at least 0.40 years more than the sample average graduation time of students at private universities. ○ If Ho is true, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is 0.40 or more years less than the sample average graduation time of students at private universities. If Ho is false, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is 0.40 or more years less than the sample average graduation time of students at private universities. If Ho is false, then there is a chance equal to the p-value that the sample average graduation time of the California state university system students is at least 0.40 years more than the sample average graduation time of students at private universities. Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. (Upload your file below.) Choose File No file chosen
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