Question

b. identify the null and alternative hypotheses?
$h_0: mu = 1.5777$
$h_a: mu = 2.7181$

c. is the original claim located in the null or alternative hypothesis?
alternative hypothesis

d. calculate your test statistic. write the result below, and be sure to round your final answer to two decimal places.

e. calculate your p - value. write the result below, and be sure to round your final answer to decimal places.

Explanation:

Step1: Recall test - statistic formula

The test - statistic for a one - sample z - test (assuming population standard deviation is known) is $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$, and for a one - sample t - test (population standard deviation unknown) is $t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$. But since the population parameters are given and no sample data is provided, we assume a z - test. However, we need sample mean, sample size and standard deviation which are not given. Let's assume we are doing a simple comparison of a hypothesized mean $\mu_0$ to a value. If we assume a standard normal distribution for simplicity (and since no other data), we can't calculate the test - statistic without more information. But if we assume we are just comparing the means in a basic way, we lack key data elements like sample statistics.

Step2: Recall p - value calculation

The p - value is calculated based on the test - statistic. For a two - tailed test with a test - statistic $z$, $p = 2(1 - \Phi(|z|))$ where $\Phi$ is the cumulative distribution function of the standard normal distribution. For a one - tailed test, if $z>0$, $p = 1-\Phi(z)$ and if $z < 0$, $p=\Phi(z)$. But without the test - statistic, we can't calculate the p - value.

Since we don't have sample size, sample mean, and standard deviation (either population or sample), we can't calculate the test - statistic and p - value.

Answer:

d. Insufficient data to calculate
e. Insufficient data to calculate