**Learning Goal:**I’m working on a statistics question and need an explanation and answer to help me learn.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible. If showing the answer in %, have two decimal places.

Answer the following problems showing your work and explaining or analyzing your results. Submit your work in a typed Microsoft Word document.

- A restaurant leaves a fishbowl on the counter for diners to drop their business cards. Once a month, a business card is pulled out to award one lucky diner with a free meal. Identify which type of sampling is used and why. (2 pts)
- A test of the effectiveness of a new curriculum could begin by dividing an area by school district, then choosing a school or set number of schools at random and sampling students from each. Identify which type of sampling is used and why. (2.5 pts)
- A survey about timekeeping might divide the population by time zone, then take 100 random samples per zone. Identify which type of sampling is used and why. (2.5 pts)
- A local TV station conducts an “Instant Poll” to predict the winner in the upcoming mayoral election. Evening news viewers were invited to phone in their votes, with the results to be announced on the late-night news. Based on the phone calls, the station predicted that Joseph Serra would win the election with 52% of the vote. They were wrong: Serra lost, getting only 46% of the vote. This faulty prediction may be the consequence of what kind of bias? (2.5 pts)
- According to Abyss Consulting, the average age of viewers of “America’s Got Talent” is 25 years old. However, the producer of the show thinks it is higher than 25.
- Write the null hypothesis Ho and alternative hypothesis Ha. (2.5 pts)
- Is this a right-tailed, left-tailed, or two-tailed test? (2 pts)

- A research analyst believes that average back-to-school spending is less than a trade group’s prediction of $606.
- Write the null hypothesis Ho and alternative hypothesis Ha. (2.5 pts)\
- Is this a right-tailed, left-tailed, or two-tailed test? (2 pts)\

- A study found that, in 2005, 12.5% of workers belonged to unions. Suppose a sample of 400 workers is collected in 2006 to determine whether union efforts to organize have increased union membership. The sample result show that 68 of the workers belonged to unions. State the null hypothesis Ho and alternative hypothesis Ha. (2.5 pts)
- Consider the null hypothesis Ho: The man is innocent of crime. Ha: The man is guilty of crime

.- What is the Type I error? (2.5 pts)
- What is the Type II error? (2.5 pts)

- Using a random sample of n = 36, the sample mean is x ̅ = 2.92. Suppose that the population standard deviation is σ=0.18.
Is the above statistical evidence sufficient to make the following claim:

μ<3

at the 5% level of significance?

- Write the null hypothesis Ho and alternative hypothesis Ha. (2.5 pts)
- Calculate the standard error. (2.5 pts)
- Calculate the z score. (2.5 pts)
- Calculate the p value. (2.5 pts)
- What is the conclusion? (2 pts)

- Using a random sample of n = 50, the sample mean is x ̅ = 297.6. Suppose that the population standard deviation is σ=12.
Is the above statistical evidence sufficient to make the following claim:

μ>295 right tail, one tail at the 1% level of significance?

- Write the null hypothesis Ho and alternative hypothesis Ha. (2.5 pts)
- Calculate the standard error. (2.5 pts)
- Calculate the z score. (2.5 pts)
- Calculate the p value. (2.5 pts)
- What is the conclusion? (2 pts)

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