State the null an alternative hypothesis in the following situations by defining

Question

State the null an alternative hypothesis in the following situations by defining the parameters used. Also, state any assumptions that you need to make to conduct the test: (a) The postal service wishes to prove that the mean delivery time for packages is less than 5 days. (b) A financial institution believes that it has an average loan processing time of less than 10 days. (c) A marketing firm believes that the average contract for a customer exceeds $50,000. (d) A Web-order company wished to test if it has improved its efficiency of operations by reducing its average response time. (e) A manufacturer of consumer durables believes that over 70% of its customers are satisfied with the product.

Explanation / Answer

Solution:-

(a) The postal service wishes to prove that the mean delivery time for packages is less than 5 days.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: > 5
Alternative hypothesis: < 5(Claim)

Note that these hypotheses constitute a one-tailed test.

(b) A financial institution believes that it has an average loan processing time of less than 10 days.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: > 10
Alternative hypothesis: < 10(Claim)

Note that these hypotheses constitute a one-tailed test.

(c) A marketing firm believes that the average contract for a customer exceeds $50,000.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: < 50,000
Alternative hypothesis: > 50,000

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

(d) A Web-order company wished to test if it has improved its efficiency of operations by reducing its average response time.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: 1< 2  
Alternative hypothesis: 1 > 2

Note that these hypotheses constitute a one-tailed test.

(e) A manufacturer of consumer durables believes that over 70% of its customers are satisfied with the product.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P < 0.70
Alternative hypothesis: P > 0.70(Claim)

Note that these hypotheses constitute a one-tailed test.

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