Question 7
When we are conducting a left-tailed hypothesis test for a proportion, if the test statistic $Z=1.62$, what is the P-value? (Round your answer to 3 decimal places.)
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Step 1 ：The P-value is the probability that we would observe a test statistic as extreme as the one we calculated, assuming the null hypothesis is true. In a left-tailed test, we are interested in the probability of observing a test statistic as extreme or more extreme in the negative direction. However, our test statistic is positive. This means that our P-value is going to be very high, specifically it's going to be greater than 0.5.

Step 2 ：To calculate the exact P-value, we need to use the cumulative distribution function (CDF) for a standard normal distribution. The CDF gives us the probability that a random variable drawn from the given distribution is less than or equal to a certain value.

Step 3 ：However, since our test statistic is positive and we are conducting a left-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme in the positive direction. This is simply 1 minus the CDF at our test statistic.

Step 4 ：Given that the test statistic Z = 1.62, we find that the P-value = 0.053.

Step 5 ：Final Answer: The P-value for a left-tailed hypothesis test with a test statistic of \(Z=1.62\) is \(\boxed{0.053}\).