STAT 300 - College 4.4 Exam UPDATED
ACTUAL QUESTIONS AND CORRECT
ANSWERS
Do cars on your street drive faster than the published speed limit? A student in a statistics class was
interested in using sample data to assess whether the mean speed of cars traveling on his street is
greater than 30 miles per hour. He lives nearby a radar speed sign which informs drivers on the speed
that they are traveling. - CORRECT ANSWER On a weekday, during the morning hours
between 8 am and 10 am, he randomly collected a sample of 20 speeds. The sample had a mean speed
of 34.6 miles per hour with a standard deviation of 8.4 miles per hour. We can assume that vehicle
speeds on this street during weekday mornings are approximately normally distributed. At the 5%
level of significance, can we conclude that the average speed of vehicles on the street during weekday
mornings is greater than the speed limit?
(A) State the null hypothesis.
Ho = - CORRECT ANSWER 30
(B) State the alternative hypothesis.
(select the correct answer from below) 30 - CORRECT ANSWER >
A student in a statistics class was interested in using sample data to assess whether the mean speed of
cars traveling on his street is greater than 30 miles per hour.
(C) Are the criteria for the approximate normality of the sampling distribution of sample means
satisfied? - CORRECT ANSWER Yes, the sample is taken from a normally distributed
population. In order to satisfy the normality criteria, the sample needs to be greater than 30, or it must
be known that the sample is drawn from a normally distributed population.
The conclusion can be drawn from the statement "We can assume that vehicle speeds on this street
during weekday mornings are approximately normally distributed."
(D) What is the sample mean? - CORRECT ANSWER 34.6
(E) What is the sample standard deviation? - CORRECT ANSWER 8.4
, (A) Calculate the test statistic for the observed sample mean. Round your answer to two decimal
places.
T= - CORRECT ANSWER 2.45
(B) Use the test statistic to find the P-value, rounded three places after the decimal.
P-value = - CORRECT ANSWER 0.012
A) How does the PP-value compare to the significance level?
P-Value < level of significance - CORRECT ANSWER <
The P-value of 0.012 (1.21%) is less than the level of significance of 0.05 (5%).
(B) What should we conclude, regarding the null and alternative hypotheses? - CORRECT
ANSWER Reject the null hypothesis and support the alternative hypothesis.
(C) Which statement best d.escribes the conclusion in the context of this scenario? - CORRECT
ANSWER There is evidence to conclude that cars are going, on average, more than 30 mph
between 8 and 10am on weekdays, on that particular street.
Identify the type of error (Type I or II) that was possible. - CORRECT ANSWER Type I. We
rejected the null hypothesis. Rejecting a null hypothesis that is actually true is a Type I error.
E) What must be true about the population mean if a Type I error occurred? - CORRECT
ANSWER Cars are going, on average, 30 mph between 8 and 10am on weekdays, on that
particular street.
(F) Would it be appropriate to generalize the results of this test to the mean speed of vehicles on the
same street during weekday evening hours? - CORRECT ANSWER No, we cannot generalize
the results to this different population. The sample only contained speeds of vehicles driven during
weekday morning hours.
Driving behavior can be different at different hours and on different days of the week. This sample is
not representative of vehicle speeds at other times and days.
ACTUAL QUESTIONS AND CORRECT
ANSWERS
Do cars on your street drive faster than the published speed limit? A student in a statistics class was
interested in using sample data to assess whether the mean speed of cars traveling on his street is
greater than 30 miles per hour. He lives nearby a radar speed sign which informs drivers on the speed
that they are traveling. - CORRECT ANSWER On a weekday, during the morning hours
between 8 am and 10 am, he randomly collected a sample of 20 speeds. The sample had a mean speed
of 34.6 miles per hour with a standard deviation of 8.4 miles per hour. We can assume that vehicle
speeds on this street during weekday mornings are approximately normally distributed. At the 5%
level of significance, can we conclude that the average speed of vehicles on the street during weekday
mornings is greater than the speed limit?
(A) State the null hypothesis.
Ho = - CORRECT ANSWER 30
(B) State the alternative hypothesis.
(select the correct answer from below) 30 - CORRECT ANSWER >
A student in a statistics class was interested in using sample data to assess whether the mean speed of
cars traveling on his street is greater than 30 miles per hour.
(C) Are the criteria for the approximate normality of the sampling distribution of sample means
satisfied? - CORRECT ANSWER Yes, the sample is taken from a normally distributed
population. In order to satisfy the normality criteria, the sample needs to be greater than 30, or it must
be known that the sample is drawn from a normally distributed population.
The conclusion can be drawn from the statement "We can assume that vehicle speeds on this street
during weekday mornings are approximately normally distributed."
(D) What is the sample mean? - CORRECT ANSWER 34.6
(E) What is the sample standard deviation? - CORRECT ANSWER 8.4
, (A) Calculate the test statistic for the observed sample mean. Round your answer to two decimal
places.
T= - CORRECT ANSWER 2.45
(B) Use the test statistic to find the P-value, rounded three places after the decimal.
P-value = - CORRECT ANSWER 0.012
A) How does the PP-value compare to the significance level?
P-Value < level of significance - CORRECT ANSWER <
The P-value of 0.012 (1.21%) is less than the level of significance of 0.05 (5%).
(B) What should we conclude, regarding the null and alternative hypotheses? - CORRECT
ANSWER Reject the null hypothesis and support the alternative hypothesis.
(C) Which statement best d.escribes the conclusion in the context of this scenario? - CORRECT
ANSWER There is evidence to conclude that cars are going, on average, more than 30 mph
between 8 and 10am on weekdays, on that particular street.
Identify the type of error (Type I or II) that was possible. - CORRECT ANSWER Type I. We
rejected the null hypothesis. Rejecting a null hypothesis that is actually true is a Type I error.
E) What must be true about the population mean if a Type I error occurred? - CORRECT
ANSWER Cars are going, on average, 30 mph between 8 and 10am on weekdays, on that
particular street.
(F) Would it be appropriate to generalize the results of this test to the mean speed of vehicles on the
same street during weekday evening hours? - CORRECT ANSWER No, we cannot generalize
the results to this different population. The sample only contained speeds of vehicles driven during
weekday morning hours.
Driving behavior can be different at different hours and on different days of the week. This sample is
not representative of vehicle speeds at other times and days.
