Let π denote the proportion of grocery store customers that use the store's club card. For a large sample z test of H0: π = .5 versus Ha: π > .5, find the P-value associated with each of the given below values of the test statistic.

yes

To find the P-value associated with each value of the test statistic, we need to use the standard normal distribution.

Step 1: Setup the hypotheses:
H0: π = 0.5 (null hypothesis)
Ha: π > 0.5 (alternative hypothesis)

Step 2: Calculate the test statistic:
The test statistic for a large sample z test when testing proportions is calculated using this formula:
z = (p̂ - π) / sqrt(π(1-π)/n)

Here, p̂ represents the sample proportion, π is the population proportion under the null hypothesis, and n is the sample size.

Step 3: Calculate the P-value:
The P-value is the probability of observing a test statistic as extreme or more extreme than the one obtained from the sample, assuming that the null hypothesis is true.

To find the P-value, we need to calculate the area under the standard normal curve to the right of the test statistic.

Using a standard normal table or a calculator, we can find the corresponding area or probability for a given z-value.

The P-value is the area to the right of the test statistic value.

Note: In this case, we are testing for the alternative hypothesis π > 0.5, so we are concerned with the upper tail of the standard normal distribution.

Without specific values for the test statistic, it is not possible to provide the P-value associated with each value. However, once you have the value of the test statistic, you can find the corresponding P-value using a standard normal table or a calculator by finding the area to the right of the test statistic.