Question

Consider $H_{0}: \mu=72$ versus $H_{1}: \mu>72 .$ A random sample of 16 observations taken from this population produced a sample mean of $75.2 .$ The population is normally distributed with $\sigma=6$. a. Calculate the $p$ -value. b. Considering the $p$ -value of part a, would you reject the null hypothesis if the test were made at a significance level of $.01 ?$ c. Considering the $p$ -value of part a, would you reject the null hypothesis if the test were made at a significance level of $.025 ?$

          Consider $H_{0}: \mu=72$ versus $H_{1}: \mu>72 .$ A random sample of 16 observations taken from this population produced a sample mean of $75.2 .$ The population is normally distributed with $\sigma=6$.
a. Calculate the $p$ -value.
b. Considering the $p$ -value of part a, would you reject the null hypothesis if the test were made at a significance level of $.01 ?$
c. Considering the $p$ -value of part a, would you reject the null hypothesis if the test were made at a significance level of $.025 ?$

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Added by Clayton D.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Kari Hasz

03/28/2023

Step 1

First, we need to calculate the test statistic (z-score) using the formula: $$ z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}} $$ where $\bar{x}$ is the sample mean, $\mu_0$ is the null hypothesis mean, $\sigma$ is the population standard deviation, and $n$ Show more…

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Consider $H_{0}: \mu=72$ versus $H_{1}: \mu>72 .$ A random sample of 16 observations taken from this population produced a sample mean of $75.2 .$ The population is normally distributed with $\sigma=6$. a. Calculate the $p$ -value. b. Considering the $p$ -value of part a, would you reject the null hypothesis if the test were made at a significance level of $.01 ?$ c. Considering the $p$ -value of part a, would you reject the null hypothesis if the test were made at a significance level of $.025 ?$

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