Question

In a study, 45 smokers were questioned about the number of hours they sleep each day. For the sample of smokers, the mean number of hours slept per day was 7.4 hours and the standard deviation was 1 hours. We wish to test the hypothesis that smokers have a different amount of sleep than the general public, who sleep for an average of 7.5 hours per day. Use ( alpha=0.05 ). a) Which one of the following is the appropriate pair of hypotheses? [ egin{array}{ll} H_{0}: mu=7.5 ; & H_{A}: mu eq 7.5 \ H_{0}: mu=7.4 ; & H_{A}: mu=7.5 \ H_{0}: mu=7.4 ; & H_{A}: mu eq 7.4 \ H_{0}: ar{x}=7.5 ; & H_{A}: ar{x} eq 7.5 \ H_{0}: ar{x}=7.4 ; & H_{A}: ar{x} eq 7.4 end{array} ] b) Calculate the standardized test statistic for this study. ( 3 mathrm{DP} ) c) Find the ( p )-value associated with the test statistic. d) From the ( p )-value you found above, select the appropriate conclusion for an hypothesis test carried out at the ( alpha=5 % ) significance level: As the ( p )-value is greater than or equal to 0.05 , there is no evidence at the 0.05 -significance level to reject ( H_{0} ) : i.e. there is no evidence that smokers sleep more or less than the general population. The observed difference is within the range we would expect due to random variation. As the ( p )-value is less than 0.05 , there is no evidence at the 0.05 -significance level to reject ( H_{0} ). The observed difference is within the range we would expect due to random variation. As the ( p )-value is less than 0.05 , we have evidence at the 0.05 -significance level that the true amount of sleep in the general population is more than 7.5 hours per night. As the ( p )-value is less than 0.05 , there is evidence to reject ( H_{0} ) at the 0.05 -significance level, which suggests that the true mean hours of sleep for smokers is different from the general population. We have evidence that ( 7.4 % ) of smokers sleep more than the general public.

          In a study, 45 smokers were questioned about the number of hours they sleep each day. For the sample of smokers, the mean number of hours slept per day was 7.4 hours and the standard deviation was 1 hours.
We wish to test the hypothesis that smokers have a different amount of sleep than the general public, who sleep for an average of 7.5 hours per day. Use ( alpha=0.05 ).
a) Which one of the following is the appropriate pair of hypotheses?
[
egin{array}{ll}
H_{0}: mu=7.5 ; & H_{A}: mu 
eq 7.5 \
H_{0}: mu=7.4 ; & H_{A}: mu=7.5 \
H_{0}: mu=7.4 ; & H_{A}: mu 
eq 7.4 \
H_{0}: ar{x}=7.5 ; & H_{A}: ar{x} 
eq 7.5 \
H_{0}: ar{x}=7.4 ; & H_{A}: ar{x} 
eq 7.4
end{array}
]
b) Calculate the standardized test statistic for this study.
( 3 mathrm{DP} )
c) Find the ( p )-value associated with the test statistic.
d) From the ( p )-value you found above, select the appropriate conclusion for an hypothesis test carried out at the ( alpha=5 % ) significance level:
As the ( p )-value is greater than or equal to 0.05 , there is no evidence at the 0.05 -significance level to reject ( H_{0} ) : i.e. there is no evidence that smokers sleep more or less than the general population. The observed difference is within the range we would expect due to random variation.
As the ( p )-value is less than 0.05 , there is no evidence at the 0.05 -significance level to reject ( H_{0} ). The observed difference is within the range we would expect due to random variation.
As the ( p )-value is less than 0.05 , we have evidence at the 0.05 -significance level that the true amount of sleep in the general population is more than 7.5 hours per night.
As the ( p )-value is less than 0.05 , there is evidence to reject ( H_{0} ) at the 0.05 -significance level, which suggests that the true mean hours of sleep for smokers is different from the general population.
We have evidence that ( 7.4 % ) of smokers sleep more than the general public.

In a study, 45 smokers were questioned about the number of hours they sleep each day. For the sample of smokers, the mean number of hours slept per day was 7.4 hours and the standard deviation was 1 hours.
We wish to test the hypothesis that smokers have a different amount of sleep than the general public, who sleep for an average of 7.5 hours per day. Use ( alpha=0.05 ).
a) Which one of the following is the appropriate pair of hypotheses?
[
eginarrayll
H0: mu=7.5 ; HA: mu
eq 7.5 H0: mu=7.4 ; HA: mu=7.5 H0: mu=7.4 ; HA: mu
eq 7.4 H0: arx=7.5 ; HA: arx
eq 7.5 H0: arx=7.4 ; HA: arx
eq 7.4
endarray
]
b) Calculate the standardized test statistic for this study.
( 3 mathrmDP )
c) Find the ( p )-value associated with the test statistic.
d) From the ( p )-value you found above, select the appropriate conclusion for an hypothesis test carried out at the ( alpha=5 % ) significance level:
As the ( p )-value is greater than or equal to 0.05 , there is no evidence at the 0.05 -significance level to reject ( H0 ) : i.e. there is no evidence that smokers sleep more or less than the general population. The observed difference is within the range we would expect due to random variation.
As the ( p )-value is less than 0.05 , there is no evidence at the 0.05 -significance level to reject ( H0 ). The observed difference is within the range we would expect due to random variation.
As the ( p )-value is less than 0.05 , we have evidence at the 0.05 -significance level that the true amount of sleep in the general population is more than 7.5 hours per night.
As the ( p )-value is less than 0.05 , there is evidence to reject ( H0 ) at the 0.05 -significance level, which suggests that the true mean hours of sleep for smokers is different from the general population.
We have evidence that ( 7.4 % ) of smokers sleep more than the general public.

Added by Sina L.

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