Questions: Question 1 1 pts A researcher wants to study what proportion of university students are working part time. They want to determine whether more than 50% of students are working part time. If p is the proportion of students that are working part time, what are the null and alternative hypotheses respectively? H 0: p>0.5 ; H 1: p=0.5 H 0: p=0.5 ; H 1: p>0.5 H 0: p<0.5 ; H 1: p>0.5 H 0: p>0.5 ; H 1: p<0.5 Question 2 1 pts A researcher wants to study what proportion of university students are working part time. They want to determine whether more than 50% of students are working part time. Which of the following are the assumptions that are made? The observations are independent and the sample size is large enough for the Central Limit Theorem The observations are drawn without replacement and the sample size is large enough for the Law of Averages The observations follow a normal distribution and the sample size is large enough for the Law of Averages The observations follow a normal distribution and the sample size is large enough for the Central Limit Theorem

Question 1 1 pts A researcher wants to study what proportion of university students are working part time. They want to determine whether more than 50% of students are working part time. If p is the proportion of students that are working part time, what are the null and alternative hypotheses respectively? H 0: p>0.5 ; H 1: p=0.5 H 0: p=0.5 ; H 1: p>0.5 H 0: p<0.5 ; H 1: p>0.5 H 0: p>0.5 ; H 1: p<0.5 Question 2 1 pts A researcher wants to study what proportion of university students are working part time. They want to determine whether more than 50% of students are working part time. Which of the following are the assumptions that are made? The observations are independent and the sample size is large enough for the Central Limit Theorem The observations are drawn without replacement and the sample size is large enough for the Law of Averages The observations follow a normal distribution and the sample size is large enough for the Law of Averages The observations follow a normal distribution and the sample size is large enough for the Central Limit Theorem
Transcript text: Question 1 1 pts A researcher wants to study what proportion of university students are working part time. They want to determine whether more than $50 \%$ of students are working part time. If $p$ is the proportion of students that are working part time, what are the null and alternative hypotheses respectively? $\qquad$ $H 0: p>0.5 ; H 1: p=0.5$ $H 0: p=0.5 ; H 1: p>0.5$ $H 0: p<0.5 ; H 1: p>0.5$ $H 0: p>0.5 ; H 1: p<0.5$ Question 2 1 pts A researcher wants to study what proportion of university students are working part time. They want to determine whether more than $50 \%$ of students are working part time. Which of the following are the assumptions that are made? The observations are independent and the sample size is large enough for the Central Limit Theorem The observations are drawn without replacement and the sample size is large enough for the Law of Averages The observations follow a normal distribution and the sample size is large enough for the Law of Averages The observations follow a normal distribution and the sample size is large enough for the Central Limit Theorem
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Solution

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Solution Steps

Solution Approach

For Question 1, the null hypothesis (H0) is typically a statement of no effect or no difference, and the alternative hypothesis (H1) is what the researcher wants to prove. Since the researcher wants to determine if more than 50% of students are working part-time, the null hypothesis should be that the proportion is 0.5, and the alternative hypothesis should be that the proportion is greater than 0.5.

For Question 2, the assumptions for a proportion hypothesis test typically include that the observations are independent and the sample size is large enough for the Central Limit Theorem to apply, which allows the sampling distribution of the sample proportion to be approximately normal.

Step 1: Null and Alternative Hypotheses

For the given research question, we define the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) as follows:

  • \( H_0: p = 0.5 \) (The proportion of students working part-time is 50%)
  • \( H_1: p > 0.5 \) (The proportion of students working part-time is greater than 50%)
Step 2: Assumptions for the Hypothesis Test

The assumptions made for conducting a hypothesis test regarding proportions include:

  • The observations are independent.
  • The sample size is large enough for the Central Limit Theorem to apply, which ensures that the sampling distribution of the sample proportion is approximately normal.

Final Answer

The null and alternative hypotheses are:

  • \( H_0: p = 0.5 \)
  • \( H_1: p > 0.5 \)

The assumptions for the hypothesis test are:

  • The observations are independent and the sample size is large enough for the Central Limit Theorem.

Thus, the answer is: \[ \boxed{H_0: p = 0.5, \; H_1: p > 0.5} \]

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