Problem

Find the P-value for a left-tailed hypothesis test with a test statistic of $z=-1.07$. Decide whether to reject $\mathrm{H}_{0}$ if the level of significance is $\alpha=0.10$. P-value $=\square($ Round to four decimal places as needed $)$

Solution

Step 1 :Given that the test statistic, \(z = -1.07\) and the level of significance, \(\alpha = 0.10\).

Step 2 :We are dealing with a left-tailed test, so we want to find the probability that a standard normal random variable is less than -1.07. This probability is the P-value.

Step 3 :We can find this probability using the cumulative distribution function (CDF) for a standard normal distribution.

Step 4 :Calculate the P-value, which is approximately 0.1423.

Step 5 :Compare the P-value with the level of significance. If the P-value is less than the level of significance, we reject the null hypothesis.

Step 6 :Since the P-value (0.1423) is greater than the level of significance (0.10), we do not reject the null hypothesis.

Step 7 :Final Answer: \(\boxed{0.1423}\)

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Source: https://solvelyapp.com/problems/19144/

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