The following data comparing wait times at two rides at Disney are listed below: Position Pirates Splash Mountain Sample Size 32 30 Average Wait Time (In Minutes) 14.68 18.77 Population Standard Deviation 11.87 16.79 What is the 98% confidence interval for the difference in wait times between pirates and splash mountain? What is the test statistic for testing to see if there is a significant difference in wait times between pirates and splash mountain?

a)

b)  

Step-by-step explanation:

Data given and notation

represent the mean for Pirates

represent the mean for Splash Mountain

represent the sample standard deviation for the sample Pirates

represent the sample standard deviation for the sample Slpash Mountain

sample size selected for Pirates

sample size selected for Splash Mountain

represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

represent the p value for the test (variable of interest)

Part a

The confidence interval would be given by:

The degrees of freedom are given by:

Since we want 98% of confidence the significance level is and , we can find in the t distribution with df =60 a critical value that accumulates 0.01 of the area on each tail and we got:

And replacing we got for the confidence interval:

Part b

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the means are equal, the system of hypothesis would be:

Null hypothesis:

Alternative hypothesis:

the statistic is given by:

(1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this: