A survey in a large class for first-year college students asked, "About how many hours do you study during a typical week?" The mean response of the 498 students was x = 15.3 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation ? = 8.5 hours for all first-year students at this university. Does the survey results provide evidence (at the 0.05 level) of students claiming to study more than 15 hours per week on average? (a) State null and alternative hypotheses in terms of the mean study time. H0: ? = 15 hours H1: ? < 15 hoursH0: ? ≤ 15 hours H1: ? > 15 hours H0: ? < 15 hours H1: ? = 15 hoursH0: ? = 15 hours H1: ? ≠ 15 hours What is the value of the test statistic z? (Give your answer to two decimal places.) z = (b) What is the P-value of the test? less than 0.001between 0.001 and 0.01 between 0.01 and 0.025between 0.025 and 0.05larger than 0.05 (c) What can we conclude about students claiming to study more than 15 hours per week on average? There is sufficient evidence that the average amount of time students claim to study is more than 15 hours per week.There is insufficient evidence that the average amount of time students claim to study is more than 15 hours per week.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A survey in a large class for first-year college students asked, "About how many hours do you study during a typical week?" The
Suppose that we know that the study time follows a
for all first-year students at this university.
Does the survey results provide evidence (at the 0.05 level) of students claiming to study more than 15 hours per week on average?
H1: ? < 15 hoursH0: ? ≤ 15 hours
H1: ? > 15 hours H0: ? < 15 hours
H1: ? = 15 hoursH0: ? = 15 hours
H1: ? ≠ 15 hours
(b) What is the P-value of the test?
(c) What can we conclude about students claiming to study more than 15 hours per week on average?
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