a sample of 16 atm transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. State the hypotheses to test whether the mean transactiontime exceeds 60 seconds
Z = (mean1-mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
90
To test whether the mean transaction time exceeds 60 seconds, we can use a one-sample t-test. Here are the null and alternative hypotheses:
Null Hypothesis (H0): The mean transaction time is equal to or less than 60 seconds.
Alternative Hypothesis (Ha): The mean transaction time exceeds 60 seconds.
Now let me explain how we arrived at these hypotheses based on the information given.
To begin, the null hypothesis assumes that there is no significant difference between the mean transaction time and 60 seconds. We are testing to see if there are grounds to reject this null hypothesis and conclude that the mean transaction time is greater than 60 seconds.
The alternative hypothesis, in contrast, asserts that the mean transaction time exceeds 60 seconds. It proposes that there is a meaningful difference between the sample mean and 60 seconds, indicating longer transaction times.
In order to conduct the actual hypothesis test, we will need to calculate the test statistic and compare it to the critical value or p-value to make our conclusion.