Question

In: Statistics and Probability

a) The head of the statistics department in a certain university believes that 70% of the...

  1. a) The head of the statistics department in a certain university believes that 70% of the department’s graduate assistantships are given to international students. A random sample of 50 graduate assistants is taken.

    What is the probability that the sample proportion pˆ will be within ±0.05 of the population proportion p?

  2. b) Recently the price of the fuel dropped to almost half of the price in previous years, a business consultant company claimed that the average car owner refilled the fuel tank when the fuel indicator showed less than 1⁄4 (0.25) of petrol left in the tank. To check the claim, 10 cars were surveyed as they entered a service station. The amount of petrol (percentage left in the tank) was measured and recorded as shown below:

0.25 0.20 0.15 0.05 0.50 0.25 0.15 0.40 0.25 0.10 Assume that the percentage of petrol remaining in the tanks is normally distributed, and the above sample standard deviation is 0.136.

Can we conclude at the 5% level of significance that the business consultant company was correct?

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Expert Solution

orchestra answered 1 year ago
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