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A simple random sample of 100 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was = 7 years with a standard deviation of s = 2 years. Assume the distribution of the time the employees have worked for the postal service is approximately Normal. The hypotheses being tested are H0: ? = 7.5, Ha: ?

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Answer:

[tex]H_{0}[/tex]: The average time postal employees have worked for the postal service is 7 years.

[tex]H_{a}[/tex]: The average time postal employees have worked for the postal service is not 7 years.

Step-by-step explanation:

We need to know the significance level to decide if the average time worked for the postal service has changed according to the the random sample of 100 postal employees working time.

Aur hypothesis would use two tailed critical region, sice the hypothesis is an equality.

The hypotheses being tested for the considered situation are stated as:

  • Null hypothesis: [tex]H_0: \mu = 7.5[/tex]
  • Alternate hypothesis:  [tex]H_A: \mu \neq 7.5[/tex]

How to form the hypotheses?

There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

We usually denote null hypothesis by [tex]H_0[/tex] and alternate hypothesis by [tex]H_A[/tex] or [tex]H_a[/tex] or [tex]H_1[/tex]

For this case, we want to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago.

Null hypothesis, therefore, will nullify any change. Thus,

  • Null hypothesis: No significant change in average time that postal employees have worked from the value of 7.5 years recorded 20 years ago.
  • Alternate hypothesis: The  average time that postal employees have worked is significantly changed from the value of 7.5 years recorded 20 years ago.

Now we need to write it symbolically.

[tex]\mu_{old} = 7.5 \: \rm years\\\\mu_{new} = ?\\\overline{x}_{new} = 7 \: \rm years[/tex]

where [tex]\overline{x}[/tex] shows sample mean and [tex]\mu[/tex] shows population mean.

Sample mean estimates population mean. From the new sample mean, we want to hypothesize about new population mean.

Thus, we get:

  • Null hypothesis: [tex]H_0: \mu = 7.5[/tex]
  • Alternate hypothesis:  [tex]H_A: \mu \neq 7.5[/tex]

where [tex]\mu = \mu_{new}[/tex] for simplicity.

Thus, the hypotheses being tested for the considered situation are stated as:

  • Null hypothesis: [tex]H_0: \mu = 7.5[/tex]
  • Alternate hypothesis:  [tex]H_A: \mu \neq 7.5[/tex]

Learn more about hypothesis formation here:

https://brainly.com/question/18831983

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