Suppose a Firm That Produces Light Bulbs Wants to Know

question 40

Essay

Suppose a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below.
-(A) Can the sample size be determined from the information above? Yes or no? If yes, what is the sample size in this case?
(B) The firm believes that the mean life is actually greater than 1500 hours, should you conduct a one-tailed or a two-tailed hypothesis test? Explain your answer, and state the appropriate null and alternative hypotheses.
(C) What is the sample mean of this data? If you use a 5% significance level, would you conclude that the mean life of the light bulbs is typically more than 1500 hours? Explain your answer.
(D) If you were to use a 1% significance level in this case, would you conclude that the mean life of the light bulbs is typically more than 1500 hours? Explain your answer.

Calculate the standard error of the mean based on the population standard deviation and sample size.

Calculate and interpret the observed z value given a sample mean, population average, and standard error.

Identify the meaning of symbols and terminology used in statistical formulas (e.g., n, μ, σ, z).

Understand the criteria for using one-sample t-tests and Z-tests.

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Definitions:

March Put

An options contract giving the holder the right to sell an asset at a specified price before or on a March expiration date.

Underlying Stock

The basic security or asset upon which derivative contracts, such as options and futures, are based.

Exercise Price

The predetermined price at which an option can be exercised, allowing the holder to buy or sell the underlying asset.

Risk-Free Rate

The theoretical rate of return of an investment with zero risk, often represented by the yield on government bonds.