Hi, I would appreciate if you could help me with these questions please.Thank you so much in advance. ### Hypothesis Testing Worksheet#### Question 1: Calculate the test statistic.- a. 4.98- b. 4.93- c. None of the other choices- d. 5.71#### Question 2: If the value of the test statistic is 5.40, calculate the p-value.- a. 0.0003- b. 0.0004- c. 0.0002- d. None of the other choices#### Question 3: If the p-value is 0.0327, state your decision.- a. Reject $ H_A $- b. Reject $ H_0 $- c. None of the other choices- d. Fail to reject $ H_0 $#### Question 4: Suppose your decision is to fail to reject $ H_0 $. Report your conclusion.- a. At a 5% significance level, we have insufficient evidence to support the celebrity's claim.- b. At a 5% significance level, we have to fail to reject the celebrity's claim.- c. At a 5% significance level, we have sufficient evidence to support the celebrity's claim.- d. At a 5% significance level, we are undecided about the celebrity’s claim. ### Example 7A celebrity claims that more than 45% of adults recognize his name. His publicist selects a random sample of 303 adults and finds that 179 recognize his name. At a 5% significance level, test the celebrity's claim. Assume that this is a Binomial experiment.#### Define the parameter of interest.- a. $ p $ = the population proportion of 179 adults who recognize the celebrity's name- b. $ p $ = the population proportion of 303 adults who recognize the celebrity's name- c. None of the other choices- d. $\hat{p} $ = the population proportion of adults who recognize the celebrity's name#### Define the random variable of interest.- a. $\hat{p} $ = the population proportion of adults who recognize the celebrity's name- b. $\hat{p} $ = the sample proportion of 303 adults who recognize the celebrity's name- c. $ p $ = the sample proportion of 179 adults who recognize the celebrity's name- d. None of the other choices#### State the null hypothesis.- a. $ p \geq 0.45 $- b. None of the other choices- c. $ p \leq 0.45 $- d. $ p > 0.45 $#### Which of the following is one of the conditions that needs to be checked to determine the distribution of the test statistic?- a. $ np \geq 10 $- b. $ n\hat{p} \geq 10 $- c. $ n(1 - \hat{p}) \geq 30 $- d. None of the other choices### Detailed Explanation:1. **Parameter of Interest:** The parameter of interest refers to the true proportion of the population that recognizes the celebrity's name. The correct option should reflect the population proportion, not the sample proportion.2. **Random Variable of Interest:** The random variable of interest refers to the sample proportion of the adults in the sample who recognize the celebrity's name. This is denoted by $\hat{p}$.3. **Null Hypothesis:** The null hypothesis is a statement that there is no effect or no difference. It is the hypothesis that is tested for possible rejection under the

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Description: Hi, I would appreciate if you could help me with these questions please.Thank you so much in advance. ### Hypothesis Testing Worksheet#### Question 1: Calculate the test statistic.- a. 4.98- b. 4.93- c. None of the other choices- d. 5.71#### Question

Given: n = 303 X = 179 Significance level = 0.05 Formula Used:

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EXAMPLE 7. A celebrity claims that more than 45% of adults recognize his name. His publicist selects a random sample of 303 adults and finds that 179 recognize his name. At a 5% significance level, test the celebrity's claim. Assume that this is a Binomial experiment. Define the parameter of interest. a. p= the population proportion of 179 adults who recognize the celebrity's name b. p = the population proportion of 303 adults who recognize the celebrity's name O c. None of the other choices o d. p = the population proportion of adults who recognize the celebrity's name Define the random variable of interest. O a. p = the population proportion of adults who recognize the celebrity's name o b. p = the sample proportion of 303 adults who recognize the celebrity's name O c.p = the sample proportion of 179 adults who recognize the celebrity's name o d. None of the other choices State the null hypothesis. O a. p0.45 O b. None of the other choices O c.pa0.45 O d.p>0.45 Which of the following is one of the conditions that needs to be checked to determine the distribution of the test statistic? O a. np 2 10 o b. np > 10 O . n(1 – p) 2 30 o d. None of the other choices

EXAMPLE 7. A celebrity claims that more than 45% of adults recognize his name. His publicist selects a random sample of 303 adults and finds that 179 recognize his name. At a 5% significance level, test the celebrity's claim. Assume that this is a Binomial experiment. Define the parameter of interest. a. p= the population proportion of 179 adults who recognize the celebrity's name b. p = the population proportion of 303 adults who recognize the celebrity's name O c. None of the other choices o d. p = the population proportion of adults who recognize the celebrity's name Define the random variable of interest. O a. p = the population proportion of adults who recognize the celebrity's name o b. p = the sample proportion of 303 adults who recognize the celebrity's name O c.p = the sample proportion of 179 adults who recognize the celebrity's name o d. None of the other choices State the null hypothesis. O a. p0.45 O b. None of the other choices O c.pa0.45 O d.p>0.45 Which of the following is one of the conditions that needs to be checked to determine the distribution of the test statistic? O a. np 2 10 o b. np > 10 O . n(1 – p) 2 30 o d. None of the other choices

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Hi, I would appreciate if you could help me with these questions please.

Thank you so much in advance.

### Hypothesis Testing Worksheet

#### Question 1: Calculate the test statistic.
- a. 4.98
- b. 4.93
- c. None of the other choices
- d. 5.71

#### Question 2: If the value of the test statistic is 5.40, calculate the p-value.
- a. 0.0003
- b. 0.0004
- c. 0.0002
- d. None of the other choices

#### Question 3: If the p-value is 0.0327, state your decision.
- a. Reject $ H_A $
- b. Reject $ H_0 $
- c. None of the other choices
- d. Fail to reject $ H_0 $

#### Question 4: Suppose your decision is to fail to reject $ H_0 $. Report your conclusion.
- a. At a 5% significance level, we have insufficient evidence to support the celebrity's claim.
- b. At a 5% significance level, we have to fail to reject the celebrity's claim.
- c. At a 5% significance level, we have sufficient evidence to support the celebrity's claim.
- d. At a 5% significance level, we are undecided about the celebrity’s claim.

### Example 7

A celebrity claims that more than 45% of adults recognize his name. His publicist selects a random sample of 303 adults and finds that 179 recognize his name. At a 5% significance level, test the celebrity's claim. Assume that this is a Binomial experiment.

#### Define the parameter of interest.
- a. $ p $ = the population proportion of 179 adults who recognize the celebrity's name
- b. $ p $ = the population proportion of 303 adults who recognize the celebrity's name
- c. None of the other choices
- d. $\hat{p} $ = the population proportion of adults who recognize the celebrity's name

#### Define the random variable of interest.
- a. $\hat{p} $ = the population proportion of adults who recognize the celebrity's name
- b. $\hat{p} $ = the sample proportion of 303 adults who recognize the celebrity's name
- c. $ p $ = the sample proportion of 179 adults who recognize the celebrity's name
- d. None of the other choices

#### State the null hypothesis.
- a. $ p \geq 0.45 $
- b. None of the other choices
- c. $ p \leq 0.45 $
- d. $ p > 0.45 $

#### Which of the following is one of the conditions that needs to be checked to determine the distribution of the test statistic?
- a. $ np \geq 10 $
- b. $ n\hat{p} \geq 10 $
- c. $ n(1 - \hat{p}) \geq 30 $
- d. None of the other choices

### Detailed Explanation:

1. **Parameter of Interest:**
The parameter of interest refers to the true proportion of the population that recognizes the celebrity's name. The correct option should reflect the population proportion, not the sample proportion.

2. **Random Variable of Interest:**
The random variable of interest refers to the sample proportion of the adults in the sample who recognize the celebrity's name. This is denoted by $\hat{p}$.

3. **Null Hypothesis:**
The null hypothesis is a statement that there is no effect or no difference. It is the hypothesis that is tested for possible rejection under the

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