Question

A critical component on a submarine has an operating lifetime that is expo- nentially distributed with mean 0.50 years. As soon as a component fails, it is replaced by a new one having statistically identical properties. What is the smallest number of spare components that the submarine should stock if it is leaving for a one-year tour and wishes the probability of having an inoperable unit caused by failures exceeding the spare inventory to be less than 0.02?

Answer 1

Answer:The value of z test statistics is 1.561.

Explanation:

We are given that a poll finds that 54% of the 600 people polled favor the incumbent.

Shortly after the poll is taken, it is disclosed that the incumbent had an extramarital affair. A new poll finds that 50% of the 1030 polled now favor the incumbent.

Let p_1 = population proportion of people who favor the incumbent in the first poll

p_2 = population proportion of people who favor the incumbent in the second poll

So, Null Hypothesis, H_0 : p_1\geq p_2 {means that his support has increased or remained same after the second poll}

Alternate Hypothesis, H_0 : p_1 < p_2 {means that his support has decreased after the second poll}

The test statistics that would be used here is Two-sample z test for proportions;

where, \hat p_1 = sample proportion of people who favor the incumbent in first poll = 54%

\hat p_1 = sample proportion of people who favor the incumbent in second poll = 50%

n_1 = sample of people in first poll = 600

n_2 = sample of people in second poll = 1030

So, the test statistics = 1.561

Hence, the value of z test statistics is 1.561.