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In testing the hypothesesH0: μ = 50HA: μ < 50we found that the standardised test statistic is Z = –1.59. Calculate the p-value.Group of answer choices0.02950.05590.11180.9441

Question

In testing the hypothesesH0: μ = 50HA: μ < 50we found that the standardised test statistic is Z = –1.59. Calculate the p-value.Group of answer choices0.02950.05590.11180.9441

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Solution

The p-value is calculated by looking up the Z-score in a standard normal distribution table or using a calculator with a normal distribution function.

The Z-score of -1.59 corresponds to a left-tail probability of 0.0561 (or 5.61%). This is the proportion of the distribution that falls to the left of Z = -1.59.

In hypothesis testing, the p-value is the probability of obtaining a result as extreme as, or more extreme than, the observed data, under the assumption that the null hypothesis is true.

Since we are testing the alternative hypothesis HA: μ < 50, we are interested in the left-tail probability. Therefore, the p-value in this case is 0.0561 or 5.61%, which corresponds to the answer choice 0.0559 (rounded to four decimal places).

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