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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.

Respuesta :

JeanaShupp

Answer: t = 1.9287

Step-by-step explanation:

Let [tex]\mu[/tex] be the average number of pages should be sent by 2-day mail instead.

As per given we have,

[tex]H_0: \mu \leq7\\\\H_a:\mu>7[/tex]

Sample mean : [tex]\overline{x}=8.52[/tex]

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 :-

[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]

[tex]t=\dfrac{8.5-7}{\dfrac{3.81}{\sqrt{24}}}\\\\=\dfrac{1.5}{\dfrac{3.81}{4.8990}}\\\\=\dfrac{1.5}{0.777712993333}=1.92873208093\approx1.9287[/tex]

Hence, the test statistics : t = 1.9287

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