1 State the null hypothesis Ho and the alternative hypothesi

1.   State the null hypothesis Ho and the alternative hypothesis Ha that would be used for a hypothesis test related to each of the following statements.

a.)   The mean age of the students enrolled in evening classes at a certain college is greater than 26 years.

b.)   The mean weight of packages shipped on Air Cargo during the past year was less than 36.7 lbs.

c.)   The mean life of incandescent bulbs is at least 750 hrs.

d.)   The mean weight of college football players is no more than 210 lbs.

e.)   The mean strength of welds by a new process is different from 570 lbs per unit area, the mean strength of welds by the new process.

There are only two possible decisions as a result of a hypothesis test.

a.)   State the two possible decisions.

b.)   Describe the conditions that will lead to each of the two decisions identified in a.).

Solution

a.)   The mean age of the students enrolled in evening classes at a certain college is greater than 26 years.

Let mu be the population mean

Ho: mu=26

Ha: mu>26

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b.)   The mean weight of packages shipped on Air Cargo during the past year was less than 36.7 lbs.

Ho: mu=36.7

Ha: mu<36.7

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c.)   The mean life of incandescent bulbs is at least 750 hrs.

Ho: mu=750

Ha: mu>750

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d.)   The mean weight of college football players is no more than 210 lbs.

Ho: mu=210

Ha: mu<210

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e.)   The mean strength of welds by a new process is different from 570 lbs per unit area, the mean strength of welds by the new process.

Ho: mu=570

Ha: mu not equal to 570

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There are only two possible decisions as a result of a hypothesis test.

a.)   State the two possible decisions.

Reject Ho and Do not reject Ho.

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b.)   Describe the conditions that will lead to each of the two decisions identified in a.).

Reject Ho when the the p-value of test statistic is less than the significant level

Do not reject Ho when the p-value of test statistic is larger than the significant level