Question

A sample of 16 atm transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the test statistic to decide whether the mean transaction time exceeds 60 seconds.

Answer 1

`t=(67-60)/((12)/(√(16)))=2.33`

Explanation:

Data given and notation

`\bar X=67` represent the sample mean

`s=12` represent the sample standard deviation

`n=16` sample size

`\mu_o =60` represent the value that we want to test

t would represent the statistic (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is higher than 60, the system of hypothesis would be:

Null hypothesis:
`\mu \leq 60`

Alternative hypothesis:
`\mu > 60`

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

`t=(\bar X-\mu_o)/((s)/(√(n)))` (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

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

`t=(67-60)/((12)/(√(16)))=2.33`