Assume That a Simple Random Sample Has Been Selected from a Normally

question 5

Essay

Assume that a simple random sample has been selected from a normally distributed population and test the
given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative
hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final
conclusion that addresses the original claim. A light-bulb manufacturer advertises that the average life for its light
bulbs is 900 hours. $$\begin{array}{l}\text { A random sample of } 15 \text { of its light bulbs resulted in the following lives in hours. }\\\begin{array} { l l l l l l l l } 995 & 590 & 510 & 539 & 739 & 917 & 571 & 555 \\916 & 728 & 664 & 693 & 708 & 887 & 849 & \\\hline\end{array}\end{array}$$ At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the
P-value method of testing hypotheses.

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Definitions:

Perfect Substitutes

Goods or services that can be used in exactly the same way, thus one can completely replace another in consumption.

Marginal Rate of Substitution

The speed at which a consumer is prepared to exchange one product for another while keeping their overall satisfaction constant.

Utility Maximizing

The process or behavior of consumers attempting to get the greatest amount of satisfaction from their consumption choices, subject to their income and the prices of goods and services.

Consumption Map

A graphical representation showing different combinations of goods or services that provide equal satisfaction or utility to a consumer.