A biologist examines 17 seawater samples for magnesium concentration. The mean magnesium concentration for the sample data is 0.252 cc/cubic meter with a standard deviation of 0.074. Determine the 80% confidence interval for the population mean magnesium concentration. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Please use the p-value approach to conduct a hypothesis test for the following problem. Please provide detailed solutions in the four steps to hypothesis testing.

The security department of a factory wants to know whether the true average time required by the night guard to walk his round is 30 minutes. If, in a random sample of 45 rounds, the night guard averaged 30.9 minutes with a standard deviation of 1.8 minutes, determine whether this is sufficient evidence to reject the null hypothesis μ=30 minutes in favor of the alternative hypothesis μ≠30 minutes. Use the 0.05 level of significance.

Suppose the local Best Buy store averages 301 customers every day entering the facility with a standard deviation of 80 customers. A random sample of 50 business days was selected. What is the probability that the average number of customers in the sample is between 290 and 310?

1. Can taking chess lessons and playing chess improve memory? The online article “The USA Junior Chess Olympics Research: Developing Memory and Verbal Reasoning” (New Horizons for Learning, April 2001) described a study in which sixth-grade students who had not previously played chess participated in a program in which they took chess lessons and played chess daily for 9 months. Each student took a memory test (the Test of Cognitive Skills) before starting the chess program and again at the end of the 9-month period. The table below shows the results for 12 randomly selected students.

Test the claim at the α = 0.01 level of significance that students who participated in the chess program achieve higher memory scores after completion of the program.

1. State the null and alternate hypotheses [3]

2. Check the assumptions [4]

3. Give the test statistic [2]

4. Give the P-value and the conclusion reached about the null hypothesis based on the P-value. [2]

5. Summarize the final conclusion in the context of the claim. [2]

1. A bag contains four quarters, one nickel, one dime, and five pennies. We reach with our hand and pull out two coins at random. What are the chances that we pull $0.15 worth of coins?

These days, delivery and carry out are pretty much the only options for our favorite restaurant food. In a random sample of 80 orders from Bob’s Burgers, 46 of them were for delivery (the rest were carry out). In a random sample of 62 orders from Pete’s Pitas, 40 were for delivery. Test the claim that customers of Bob’s Burgers and Pete’s Pitas are equally likely to choose delivery, using an appropriate hypothesis test. Your write-up should include statements of the null and alternative hypotheses, the relevant test statistic, the corresponding p-value, and an appropriate conclusion regarding the original claim.

1. In a study of habits of undergraduate students, a researcher sampled 53 students and found that the mean number of classes missed over the course of a school year was 18. Assume the population standard deviation, σ = 5.7.
   1. (5 points) Calculate the 95% confidence interval for the mean number of classes missed during the school year by undergraduate students.

2. (2 points) If the researcher had sampled 75 students, would the margin of error be larger or smaller?

3. (2 points) If the researcher used a 90% confidence level instead of 95%, would the margin of error be larger or smaller?

What are some approaches to assigning probability? Which could be labeled as difficult to understand? Why?

1. A popular professor wants to construct a 90% confidence interval with a margin of error = 0.03 on the proportion of students that make a thorough “cheat sheet” for her statistics tests.
   1. (4 points) Through experience, the professor estimates that about 42% of students make thorough “cheat sheets.” Using this estimate for the sample proportion, how many students should the professor sample?

2. (4 points) How many students should the professor sample if no estimate is available?

Why is Cohen's d an important statistic to compute for a hypothesis test?

In a random sample of 115 trombone players, 13 were female. Construct a 99% confidence interval for the proportion of trombone players that are female.

The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 70 inches and a standard deviation of 10 inches. If represents the average amount of snowfall in 5 years, find k such that P(<k) = 0.85. Round your answer to 3 decimal places.

The SAT scores for students are normally distributed with a mean of 1000 and a standard deviation of 200. What is the probability that a sample of 36 students will have an average score between 970 and 1010? Round your answer to 3 decimal places.

Required information

[The following information applies to the questions displayed below.]

Multiple Choice

• H₀: μ ≤ 6.7 ; H₁: μ > 6.7

• H₀: μ = 6.7 ; H₁: μ ≠ 6.7

• H₀: μ > 6.7 ; H₁: μ = 6.7

• H₀: μ ≥ 6.7 ; H₁: μ < 6.7

Multiple Choice

• Reject H₀ if z < -1.645

• Reject H₁ if z > -1.645

• Reject H₀ if z > -1.645

• Reject H₁ if z < -1.645

Multiple Choice

• Reject H₀

• Cannot reject H₀

Question 2

A study of the impact of graphical quality and age on time spent playing a computer game. Researchers record the time, in minutes, that children spent playing three computer games: one with minimal 2D graphics, one with high 2D graphic quality, and one with 3D graphic quality. Researchers also note the age group of each child: Under 10, 10 to 13, and over 13.

Write the null and alternative hypotheses for both factors and for their interaction.

Question 4

A study of the number of hits a video gets on YouTube based on the type of video (humorous, inspirational, musical, and informational) and on the length of the video (under 1 minute, 1 to 5 minutes, more than 5 but less than 10, 10 or more minutes).

Write the null and alternative hypotheses for both factors and for their interaction.