This question is worth 2 points. You will use a statistical program of your choice (Statcrunch, Excel, etc) to find the following: A fashion researcher who studies viral style trends is investigating the popularity of wearing socks with sandals on social media. She randomly selects a sample of 50 Instagram posts tagged with #sockandsandals and finds that, on average, each post received 1,850 likes, with a standard deviation of 470 likes. Construct a 95% confidence interval to estimate the true mean number of likes for Instagram posts featuring this trend. What is the lower bound? (It is sometimes referred to as the “lower limit) Round your answer to 2 decimal places.

As part of a Master’s thesis project, a mathematics teacher is interested in the effects of two different teaching methods on mathematics achievement. She randomly chooses one class of students to learn an algebraic concept using traditional methods and another class of students to learn the same algebraic concept using manipulatives. The teacher then compares their test scores. Determine whether the samples are dependent or independent.

Have we met the normality requirement for this test? 

A manufacturer claims that their machine can produce at least 100 widgets per hour. However, you suspect that the machine produces more than 100 widgets per hour on average. You want to test if the machine’s output is greater than 100 widgets per hour. Is this a left-tailed, right-tailed, or two-tailed test? 

Provide an appropriate response.Find the variance of the binomial distribution for which n = 40 and p = 0.6.

A recent study shows that the average amount of sleep high school students get on a school night is 6.8 hours, with a standard deviation of 1.2 hours. Angelica is a high school student who reported getting 9.1 hours of sleep on a typical school night.  What is Angelica’s z-score? Round your answer to two decimal places.

Determine whether the distribution represents a probability distribution. If not, identify any requirements that are not satisfied. x P(x) 1 .03 2 .61 3 .15 4 .32

Determine whether the distribution represents a probability distribution. If not, identify any requirements that are not satisfied. x P(x) 1 .31 2 .06 3 .77 4 .81

A dentist is evaluating whether a new whitening toothpaste works better than a standard toothpaste. She recruits married couples and randomly assigns one partner in each couple to use the new toothpaste and the other to use the standard toothpaste. After three weeks, she compares the results within each couple. Determine whether the samples are dependent or independent.

Find the variance of the binomial distribution for which n = 70 and p = 0.3.