A survey was conducted to determine whether the hours of sleep per night are independent of age.
a.) Hence, the appropriate test of hypothesis would be :
Option d
Ho: Hours of sleep per night is independent of age
Ha: Hours of sleep per night is not independent of age.
To test the above hypothesis we make use of the Pearsonian chi-square test.
The value of the test-statistic is given by :
Where Oij are the observed cell frequencies and Eij are the expected cell frequencies if they both are to be independent.
If N be the total number of observations,
Eij=Npi.* p.j
where pi.=sum of all observations for the ith row / N
p.j=sum of all observations for the jth column / N
The contingency table below provides the following information: the observed cell totals, (the expected cell totals) and [the chi-square statistic for each cell].
Hence, the observed value of the test statistic is 3.8946 and the p-value is 0.2731
Since the p-value is greater than our chosen level of significance which is 0.05, so we cannot reject the null hypothesis and conclude that :
Option d:
Do not reject Ho.Hours of sleep per night and age are independent.
b.) To calculate the percentages we use the row totals from the table above.
Hence,
Fewer than 6 = 70/500*100 = 14%
6 to 6.9 = 117/500*100 = 23.4%
7 to 7.9 = 152/500*100 = 30.4%
8 or more = 161/500*100 = 32.2%
A survey was conducted to determine whether hours of sleep per night are independent of age....
A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. sample data follow. Age...
A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow. Hours...
to of age A options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the options: age 39 or younger and age 40 or older. Sample data follow. 6 to 6.9 7 to 7.9 of age. Ha: Hours of sleep per night is not mutually exclusive from age. Find the value of the test statistic. (Round your answer to three decimal places.) What Is the p-value? (Round your answer to...
The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older Age 49 or younger 50 or older a. Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use α =...
The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older Hours of Sleep 6 to 6.9 63 57 Fewer than 6 Age 49 or younger 50 or older a. Conduct a test of independence to determine whether the hours...
The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older. Hours of Sleep 6 to 6.9 Age Fewer than 7 to 7.9 8 or more Total 38 74 49 or younger 50 or older a. Conduct a test of...
The National Sleep Foundation used a survey to determine whether hours of sleeping per night are Independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of Individuals age 49 and younger and for a sample of individuals age 50 and older. Hours of Sleep 6 to 6.9 65 Age 19 or younger 50 or older a, conduct a test of independence to determine whether the hours of sleep on weeknights...
A survey cunducted o de errm'าษ whether hours u eep per r "yht dre r dependent of dye. A sample U Individuals was e'sked o indicate he nur er u huurs o sleep per mqht with ca euricd options: ev e u dn 6 hours, 6 to 6.9 hours 7 to 7.9 hours dnd ε huurs or more. Later in the survey, the individuas were asked to indicate their age with categorical options: age 39 or yournger and age 40...
CheckK MV Work The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older. Age 49 or younger 50 or older a. Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age....
The recommended number of hours of sleep per night is 8 hours, but everybody "knows" that the average college student sleeps less than 7 hours. The number of hours slept last night by 10 randomly selected college students is listed below. Complete the following hypothesis test: Ho: μ = 7, Ha: μ < 7, α = 0.05. 7.9 6.2 6.8 7 6.9 5.6 5.2 5.7 7.3 5.5 (a) Find t. (Give your answer correct to two decimal places.) (ii) Find...