Question

Faced with rising fax costs, a firm issued a guideline that transmissions of 7 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 7 or below. The firm examined 24 randomly chosen fax transmissions during the next year, yielding a sample mean of 8.52 with a standard deviation of 3.81 pages. Find the test statistics.

Answer 1

Answer: t = 1.9287

Explanation:

Let
`\mu` be the average number of pages should be sent by 2-day mail instead.

As per given we have,

`H_0: \mu \leq7\\\\H_a:\mu>7`

Sample mean :
`\overline{x}=8.52`

Sample standard deviation : s=3.81

sample size : n= 24

Since , the sample size is less than 30 and populations standard deviation is unknown , so we use t-test.

The test statistic for population mean :-

`t=\frac{\overline{x}-\mu}{(s)/(√(n))}`

`t=(8.5-7)/((3.81)/(√(24)))\\\\=(1.5)/((3.81)/(4.8990))\\\\=(1.5)/(0.777712993333)=1.92873208093\approx1.9287`

Hence, the test statistics : t = 1.9287