Must use the following Technology links/ calculators when you need to find information about a Confidence Interval, Hypothesis Test, Means, or Standard Deviations. Use the following calculators
Confidence Intervals for Means:
https://www.wolframalpha.com/input/?i=t-interval
Hypothesis Testing for Means:
https://www.wolframalpha.com/input/?i=t-test
Calculator Soup Descriiptive Statistics Calculator:
https://www.calculatorsoup.com/calculators/statistics/descriiptivestatistics.php
1. According to the US Department of Agriculture, the average amount of fresh apples consumed per person in the US during the year 2019 was approximately 9.8 pounds. Suppose a research group suspects that the average amount of fresh apples consumed per person is higher in Washington state, which is known for its delicious apples. Suppose the research group took data for a year from a random sample of 35 people in Oregon state and found that the average amount of fresh apples consumed by their sample was 12.5 pounds with a standard deviation of 4.1 pounds. Suppose also that the distribution of the amount of fresh apples of the sample participants was unimodal and roughly symmetric.
a. Define a parameter for hypothesis testing and write the null hypothesis and alternative hypothesis for this study.
b. Show that the necessary conditions (Randomization Condition, 10% Condition, Nearly Normal Condition) are satisfied to perform a hypothesis test. Briefly explain how each of the three conditions are satisfied.
c. Perform the hypothesis test and find the P-value. (To show your work: Write down the name of the calculator you are using and what values you are entering into the calculator.)
d. Do these study results provide strong evidence that the average amount of fresh apples consumed by people in Washington State is higher than 9.8 pounds? Briefly explain how you know.
Suppose a very large company claims that 94% of its employees are satisfied with their pay and benefits. A study is conducted by an independent researcher to see if the percentage of employees for that company that are satisfied with their pay and benefits is less than the company claims.
The study found a random sample of 42 employees from that company and the result of their hypothesis testing was a P-value of 0.168 with 90.5% of the sample saying they were satisfied with their pay and benefits.
Interpret the meaning of this P-value in this context. Tips for this problem:
o I am asking you to tell me what the P-value of 0.168 tells us about the particular values of 94% and 90.5% in this scenario. (Keep in mind that P-values are probabilities. Tell me exactly what this P-value is the probability of in the context of the employees.)
o I am not asking for whether you reject H0 or fail to reject H0.
