The student union is conducting a study of the sleep habits of year one and two students. A random sample of 21 year one students slept an average of 7.5 hours per night, with a standard deviation of 1.2 hours. A sample of 18 year two students slept an average of 6.4 hours per night, with a standard deviation of 1.5 hours. If needed, assume that the number of hours slept per night is normally distributed. Is there significant evidence to show that, on average, year one students sleep more than half an hour longer than year two students? a) Define the parameter(s) of interest using the correct notation. Then, state the null and alternative hypotheses for this study. b) Calculate the observed value of the test statistic. State the distribution (and degrees of freedom if needed) it follows. c) Compute the p-value or provide a range of appropriate values for the p-value. d) State the strength of evidence against the null hypothesis. e) Using the significance level α = 0.05, state your conclusions regarding the sleep habits of year one and two students.
The student union is conducting a study of the sleep habits of year one and two students. A random sample of 21 year one students slept an average of 7.5 hours per night, with a standard deviation of 1.2 hours. A sample of 18 year two students slept an average of 6.4 hours per night, with a standard deviation of 1.5 hours. If needed, assume that the number of hours slept per night is
a) Define the parameter(s) of interest using the correct notation. Then, state the null and alternative hypotheses for this study.
b) Calculate the observed value of the test statistic. State the distribution (and degrees of freedom if needed) it follows.
c) Compute the p-value or provide a
d) State the strength of evidence against the null hypothesis.
e) Using the significance level α = 0.05, state your conclusions regarding the sleep habits of year one and two students.
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