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Frequency Distribution and Sampling: Sampling Plan Analysis

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1. 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why

2. The name of each contestant is written on a separate card, the cards are placed in a bag, and three names are picked from the bag. Identify which type of sampling is used and why

3. An education expert is researching teaching methods and wishes to interview teachers from a particular school district. She randomly selects ten schools from the district and interviews all of the teachers at the selected schools. Does this sampling plan result in a random sample? Simple random sample? Explain.

4. A polling company obtains an alphabetical list of names of voters in a precinct. They select every 20th person from the list until a sample of 100 is obtained. They then call these 100 people. Does this sampling plan result in a random sample? Simple random sample? Explain.

5. The personnel manager at a company wants to investigate job satisfaction among the female employees. One evening after a meeting she talks to all 30 female employees who attended the meeting. Does this sampling plan result in a random sample? Simple random sample? Explain.

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Solution Summary

Calculations are provided for (1) and discussion is provided for (2) through (5) in 251 words in this tutorial.

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Random Sampling Distribution Test

An automobile manufacturer advertises that the mean petrol consumption of its new hybrid car does not exceed 4.6 litres per 100 km. An independent company decides to test the manufacturer's claim by selecting a random sample of 16 vehicles and measuring the consumption of each. They have found that the petrol consumptions in litres per 100 km of those vehicles are as follows:
4.7 4.9 4.4 4.5 4.6 4.7 4.7 4.8 4.9 4.3 5.0 4.6 4.7 4.9 4.8 5.1

a) Perform a hypothesis test at the 5% level to see if there is evidence to support the manufacturer's claim.

b) State the distributional assumption required for the test in part (a) to be valid, and use an appropriate plot to test the assumption. With reference to your plot, briefly explain why the assumption is or is not satisfied.

c) Based on your answers to parts a) and b), should the manufacturer be reported to a fair trading commission for misleading advertising? Briefly explain your decision.

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