Question

Inference Project - Roll a Die Data (Perform an experiment to obtain data and perform a hypothesis test of your results)

1. For this project you will need to

• Give an explanation of how you created/obtained your data and who/what it is about. Please be specific about your process.
• Give the population your sample comes from or if you are compare your sample to a given known value.
• Give the sample statistic (proportion or mean) of the variable you are using.
• Check to make sure your data meets the conditions for using the Central Limit Theorem.
  • If it doesn't meet the conditions then explain why you couldn't meet the conditions. (You still need to complete the rest of the project, but your results will not be accurate.)
• Confidence intervals
  • Make at least 2 confidence intervals for 2 different confidence levels that have the same sample size and same sample proportion:
    • Either include your calculations or your StatCrunch window
    • Interpret them in context of the data.
    • State both margin of errors
    • Explain why the intervals are different. Compare the widths and margin of errors and explain why one of them is larger than the other based on the confidence level.
  • Explain what would happen to the margin of error or interval width if you increased/decreased your sample size. Why does the margin of error get smaller/larger?
  • 2. Perform a hypothesis test then: (Make sure you give all the steps as shown in your book.)
    • State the hypothesis (Be sure to decide what you think the appropriate hypothesis should be). Write the hypothesis in both words and symbols
    • Make sure you include a picture of your applet window or your calculations if you are doing this by hand
    • Interpret the test statistic in context of the data.
    • Give and interpret the level of significance in context of the data.
    • Interpret the p-value in context of the data.
    • Write a conclusion of the hypothesis test in context of your data
• 3. Write a paragraph about your findings.
  • Make sure you write about both the confidence intervals and the hypothesis tests.
  • You may be able to tell if your confidence interval agrees with the conclusion of your hypothesis test. (Is the
    Po
    from your hypothesis test in your confidence interval?)

Answer 1

As per HomeworkLib policy only 4 question is answered.

Since the sample as

80, 80, 79, 78, 78, 77, 76, 76, 76, 76, 76, 75, 75, 75, 74, 74, 74, 73, 73, 72, 72, 72, 72, 72, 72, 71, 71, 71, 71, 71, 71, 70, 70, 70, 70, 70, 69, 69, 69, 68, 68, 68, 68, 68, 67, 67, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 64, 64, 64, 64, 64, 64, 64, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 62, 62, 62, 62, 62, 62, 62, 62, 62, 61, 61, 61, 61, 61, 61, 61, 60, 60, 60, 60, 60, 60, 60, 59, 59, 59, 59, 59, 59, 58, 58, 58, 58, 58, 58, 58, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 55, 55, 55, 55, 55, 55, 55, 55, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 53, 53, 53, 53, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 51, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 49, 49, 49, 49, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 46, 46, 46, 45, 45, 45, 45, 44, 44, 44, 44, 44, 43, 43, 43, 42, 42, 42, 42, 42, 42, 42, 42, 42, 41, 40, 40, 40, 39, 39, 39, 38, 37, 37, 37, 36, 36, 36, 36, 35, 35, 35, 34, 34, 34, 33, 32, 31, 30, 29

Mean=56.2565

Sample standard deviation=11.2288

a) Since 51 scored B hence proportion scored B as

51/269=0.1896

b)

Standard error of the mean = SEM = √x(N-x)/N³ = 0.024

α = (1-CL)/2 = 0.050

Standard normal deviate for α = Z_α = 1.645

Lower bound = P - (Z_α*SEM) = 0.1501

Upper bound = P + (Z_α*SEM) = 0.2291

c) Could not understand what actually question is wether it is hypothesis test or something else. Please write the correct question in comment box .

d) We can be 90 % confident that the proportion of B grade for population lies between (o.1501 to 0.2291)