In one year, an online travel agency reported that summer travelers booked their airline reservations an average of 74.4 days i
n advance. A random sample of 40 summer travelers in a later year was selected, and the number of days travelers booked their airline reservations in advance was recorded. The data are shown in the accompanying table.
69 76 82 65 60
79 74 75 89 68
87 86 92 56 84
79 60 71 85 86
73 71 92 76 78
69 75 58 63 55
72 85 68 86 74
67 67 54 77 77
A. Perform a hypothesis test using \alpha=0.02 to determine if the average number of days reservations are booked in advance has changed between the years.
B. Determine the critical value(s)
C. Should we reject the null hypothesis?
D. What is the p-value?
69 76 82 65 60
79 74 75 89 68
87 86 92 56 84
79 60 71 85 86
73 71 92 76 78
69 75 58 63 55
72 85 68 86 74
67 67 54 77 77
A. Perform a hypothesis test using \alpha=0.02 to determine if the average number of days reservations are booked in advance has changed between the years.
B. Determine the critical value(s)
C. Should we reject the null hypothesis?
D. What is the p-value?
1 answer:
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Answer:
a) For this case we can use the following R code to construct the qq plot
> data<-c(28.8, 24.4, 30.1, 25.6, 26.4, 23.9, 22.1, 22.5, 27.6, 28.1, 20.8, 27.7, 24.4, 25.1, 24.6, 26.3, 28.2, 22.2, 26.3, 24.4)
# The above line is in order to store the data in a vector
> qqnorm(data, pch = 1, frame = FALSE)
# The line above is in order to calculate the quantiles from the data assumin Normal distribution
> qqline(data, col = "steelblue", lwd = 2)
# The line above is in order to put a line for the theoretical dsitribution
The result is on the figure attached.
b) For this case as we can see on the figure attached the calculated quantiles are not far from the theorical quantiles given byt the straaigth blue line so then we can conclude that the distribution seems to be normal.
Step-by-step explanation:
For this case we have the following data:
28.8, 24.4, 30.1, 25.6, 26.4, 23.9, 22.1, 22.5, 27.6, 28.1, 20.8, 27.7, 24.4, 25.1, 24.6, 26.3, 28.2, 22.2, 26.3, 24.4
The quantile-quantile or q-q plot is a graphical procedure in order to check the validity of a distributional assumption for a data set. We just need to calculate "the theoretically expected value for each data point based on the distribution in question".
If the values are asusted to the assumed distribution, we will see that "the points on the q-q plot will fall approximately on a straight line"
For this case our distribution assumed is normal.
Part a
For this case we can use the following R code to construct the qq plot
> data<-c(28.8, 24.4, 30.1, 25.6, 26.4, 23.9, 22.1, 22.5, 27.6, 28.1, 20.8, 27.7, 24.4, 25.1, 24.6, 26.3, 28.2, 22.2, 26.3, 24.4)
# The above line is in order to store the data in a vector
> qqnorm(data, pch = 1, frame = FALSE)
# The line above is in order to calculate the quantiles from the data assuming Normal distribution (0,1)
> qqline(data, col = "steelblue", lwd = 2)
# The line above is in order to put a line for the theoretical distribution
The result is on the figure attached.
Part b
For this case as we can see on the figure attached the calculated quantiles are not far from the theorical quantiles given byt the straaigth blue line so then we can conclude that the distribution seems to be normal.
