Homser Lake, Oregon, has an Atlantic salmon catch-and-release program that has been very successful. The average fisherman's catch has been $$ \mu=8.4 $$. Atlantic salmon per day. Suppose that a new quota system restricting the number of fishermen has been put into effect this season. A random sample of fishermen gave the following catches per day: $$ 11,6,11,11,5,2,1,7,7,8,6,2,12,13 $$ Assuming the catch per day has an approximately normal distribution, does the sample indicate at a 0.1 level of significance that the population average catch per day is now different from 8.4 ? A) Use a calculator with the "Stats" feature to find $$ \bar{x} $$ and $$ s $$. (Round your answer to 2 decimal places). $$ \begin{array}{l} \bar{x}=7.29 \ s=3.93 \end{array} $$ B) State the Null and Alternate hypotheses. $$ \begin{array}{l} H_{0}: \mu=8.4 ; H_{1}: \mu8.4 \ H_{0}: \mu8.4 ; H_{1}: \mu=8.4 \ H_{0}=\mu \neq 8.4: H_{1}: \mu=8.4 \ H_{0}=\mu=8.4: H_{1}: \mu

Question

Homser Lake, Oregon, has an Atlantic salmon catch-and-release program that has been very successful. The average fisherman's catch has been $$ \mu=8.4 $$. Atlantic salmon per day. Suppose that a new quota system restricting the number of fishermen has been put into effect this season. A random sample of fishermen gave the following catches per day: $$ 11,6,11,11,5,2,1,7,7,8,6,2,12,13 $$ Assuming the catch per day has an approximately normal distribution, does the sample indicate at a 0.1 level of significance that the population average catch per day is now different from 8.4 ? A) Use a calculator with the "Stats" feature to find $$ \bar{x} $$ and $$ s $$. (Round your answer to 2 decimal places). $$ \begin{array}{l} \bar{x}=7.29 \ s=3.93 \end{array} $$ B) State the Null and Alternate hypotheses. $$ \begin{array}{l} H_{0}: \mu=8.4 ; H_{1}: \mu>8.4 \ H_{0}: \mu>8.4 ; H_{1}: \mu=8.4 \ H_{0}=\mu \neq 8.4: H_{1}: \mu=8.4 \ H_{0}=\mu=8.4: H_{1}: \mu<8.4 \ H_{0}: \mu=8.4 ; H_{1}: \mu \neq 8.4 \end{array} $$ C) Is this a (left-tail, right-tail, one-tail, two-tail) test? one-tail two-tail left-tail right-tail D) Accurate to 3 decimal places, find the $$ t^{\star} $$ value of the sample. $$ -1.057 $$ E) Find the degree of freedom of the sample. $$ 13 $$ F) Accurate to 4 decimal places, what's the p-value of the sample? $$ 0.3072 \times $$ G) How does p-value compare to 0.1 ? And does this sample give strong evidence to reject $$ H_{0} $$ ? p -value $$ <0 $$-1, No. $$ p $$-value $$ \geq 0-1 $$, No. p -value $$ <0 $$-1, Yes $$ p $$-value $$ \geq 0 $$-1, Yes.

UpStudy AI · Accepted Answer

**A)**  
The calculator gives  
$$
\bar{x}=7.29 \quad \text{and} \quad s=3.93.
$$

**B)**  
Since we want to test if the average catch is now different from $$8.4$$ (i.e. a change in either direction), we use the two‐tail hypotheses:  
$$
H_{0}: \mu=8.4 \quad \text{and} \quad H_{1}: \mu\neq 8.4.
$$

**C)**  
This is a two–tail test.

**D)**  
The computed $$t^\star$$ value is  
$$
t^\star=-1.057.
$$

**E)**  
The degrees of freedom are given by  
$$
\text{df}=n-1=14-1=13.
$$

**F)**  
For a two–tail test with $$t^\star=-1.057$$ and 13 degrees of freedom, the p–value is approximately  
$$
\text{p–value}=0.3072.
$$

**G)**  
Since the p–value (approximately $$0.3072$$) is greater than the significance level $$0.1$$, there is not strong evidence to reject $$H_0$$.
**A)** The average catch per day is $$7.29$$ and the standard deviation is $$3.93$$. **B)** The hypotheses are: $$ H_{0}: \mu=8.4 \quad \text{and} \quad H_{1}: \mu\neq 8.4 $$ **C)** This is a two-tail test. **D)** The $$t^\star$$ value is $$-1.057$$. **E)** The degrees of freedom are $$13$$. **F)** The p-value is approximately $$0.3072$$. **G)** Since the p-value ($$0.3072$$) is greater than $$0.1$$, there is not enough evidence to reject $$H_0$$.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Statistics Questions