Consider the following competing hypotheses and accompanying sample data.

$$\begin{aligned} &H_0: \rho_S \leq 0 \\ &H_A: \rho_S>0 \end{aligned} \quad r_S=0.64 \text { and } n=50$$

a. What is the value of the test statistic and its associated $p$-value? Assume the normal approximation for $r_s$.

b. At the $1 \%$ significance level, what is the conclusion?

What is the formula for the $t$ statistic for a significance test for $\mu_1-\mu_2$?

For one binomial experiment, 200 binomial trials produced 60 successes. For a second independent binomial experiment, 400 binomial trials produced 156 successes. At the 5% level of significance, test the claim that the probability of success for the second binomial experiment is greater than that for the first. Compute $\hat{p}_{1}-\hat{p}_{2}$ and the corresponding sample test statistic.

What does a negative test statistic mean ?

Write the series in summation notation. Use the index $i$ and let $i$ begin at $1$.

$$\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\cdots$$

Explain how to find $F$ test statistic on $TI-84$ calculator?

What value is estimated with a confidence interval using the $t$-statistic?

How to calculate $p$-value from $F$ statistic in $R$?

Which process line should be built for a new chemical? The expected market for the chemical is 20 years. A 20% rate is used to evaluate new process facilities, which are compared with present worth. How much does the better choice save? $$ \begin{matrix} \text{ } & \text{First Cost} & \text{O&M Cost/year} & \text{Salvage} & \text{life}\\ \text{A} & \text{\$18M} & \text{\$5M} & \text{\$4M} & \text{10 years}\\ \text{B} & \text{ 25M} & \text{ 3M} & \text{ 6M} & \text{20 years}\\ \end{matrix} $$

In this exercise, express given sum using summation notation. Use $1$ as the lower limit of summation and $i$ for the index of summation.

$$1+3+5+\cdots+(2 n-1)$$

To test $H_{0}: \sigma=0.35$ versus $H_{1}: \sigma<0.35$, a random sample of size n=41 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s=0.23, compute the test statistic. (b) If the researcher decides to test this hypothesis at the $\alpha$=0.01 level of significance, determine the critical value. (c) Draw a chi-square distribution and depict the critical region. (d) Will the researcher reject the null hypothesis? Why?

How can I find $p$ value from $f$ statistic ?

The lease term is noncancelable period for which a lessee has the right to use an underlying asset, modified by any renewal or termination options that are “reasonably certain” to be exercised, or not exercised. Options whose exercise is under the control of the lessor are automatically included. The FASB Accounting Standards Codification represents the single source of authoritative U.S. generally accepted accounting principles.

1. Access the FASB’s Codification Research System at the FASB website (www.fasb.org). Determine the specific eight-digit Codification citation (XXX-XX-XX-X) that describes the guidelines for determining when the lessee should reassess the term of the lease.

2. List the disclosure requirements.

What is the formula for the chi-square test statistic?