Question

a. what type of test will be used in this problem? (a test for the mean using the t - distribution (t - test))
b. identify the null and alternative hypotheses?
$h_0: mu$
$h_a: mu$
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.
2.07
e. calculate your p - value. write the result below, and be sure to round your final answer to four decimal places.

Explanation:

Step1: Recall p - value formula for one - tailed t - test

For a one - tailed t - test with test statistic $t = 2.07$ and degrees of freedom (not given, assume a large enough sample or known degrees of freedom situation), we use the t - distribution table or a statistical software/ calculator function. If using a calculator like a TI - 84 Plus, we use the tcdf function. For a right - tailed test with $t = 2.07$, we calculate $P(T>2.07)$.
Using a t - distribution table or software, if the degrees of freedom are large (or using a standard normal approximation for large samples which is similar in the right - tail for large values), we know that the p - value is the area under the t - distribution curve to the right of the test statistic.
The p - value for a right - tailed t - test with $t = 2.07$ can be found as follows:
If using a TI - 84 Plus: tcdf(2.07, 1E99, df) (where df is degrees of freedom. For large df, it is close to the standard normal right - tail area). For a large enough df, we can approximate using the standard normal. The standard normal approximation: $P(Z > 2.07)=1 - P(Z\leq2.07)$.
From the standard normal table, $P(Z\leq2.07) = 0.9808$. So $P(Z > 2.07)=1 - 0.9808=0.0192$.

Step2: Round the p - value

We are asked to round the p - value to four decimal places.

Answer:

0.0192