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? $h_0: mu = 1576$ $h_a: mu
eq 1576$ c. is the original claim located in the null or alternative hypothesis? null hypothesis d. calculate your test statistic. write the result below, and be sure to round your final answer to two decimal places. 0.39 e. calculate your p - value. write the result below, and be sure to round your final answer to decimal places.

Explanation:

Step1: Recall t - test p - value formula

For a two - tailed t - test with test statistic $t$, the p - value is $2P(T > |t|)$ where $T$ follows a t - distribution with appropriate degrees of freedom. Here, $t = 0.39$.

Step2: Use t - distribution table or software

We use a t - distribution table or statistical software (e.g., R: 2(1 - pt(0.39, df)), Python: 2(1 - scipy.stats.t.cdf(0.39, df)) where df is the degrees of freedom. Assuming a large enough sample or known degrees of freedom, using a standard normal approximation for large degrees of freedom (since for large df, t - distribution approaches normal), we know that $P(Z>0.39)=1 - P(Z < 0.39)$. From the standard normal table, $P(Z < 0.39)=0.6517$, so $P(Z>0.39)=1 - 0.6517 = 0.3483$. Then the p - value for a two - tailed test is $2\times0.3483 = 0.6966\approx0.70$.

Answer:

0.70