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Exam 1 review Worksheet STAT218-001 Spring 2018

I.

In a large-scale, cost of living survey undertaken last month in a city, weekly grocery expenses for families with one or two children were found to have a mean of $148. To investigate the current situation, a random sample of 100 families with one or two children were asked their last week’s grocery bills. The sample mean grocery expenses per week was $150 with a standard deviation of $22. Is there any evidence that the weekly grocery expenses for families with one or two children has changed since last month?

1. What is the population of interest? The families with children 2. Was the sample collected randomly? What does that imply in terms of the conclusions we draw? Yes, it ensures that every sample is equally likely to be the sample selected from the population. 3. What is the variable? Is it categorical or quantitative? Number of Children- it is quantitative. 4. In words, what is the parameter of interest? What symbol do we use for this parameter? μ: The long run mean of the number of children in a family. 5. What is the statistic? What symbol do we use for this? x = $150 6. Is the validity condition for the Theory Based Approach met for this situation? Why or why not? Yes, because there is a sample size of above 20. 7. Using the Theory Based Approach, conduct a formal hypothesis test using standardized statistic. Use α =0.05 . The critical values for one sided test are 1.6 and -1.6, and that for two-sided test are 2 and -2. 1) Ho: μ = $148 Ha: μ ≠ $148 2) α =0.05 Since it is two tailed CV= 2 and -2 3) t = 150-148/ 22/√100 = 0.91 4) -2 .53 2) α =0.01 since it is one sided use 2.3 and -2.3 3) z = .58 - 0.53/ √1-0.53/680 = 2.61 4) 2.61> 2.3 Reject Null Hypothesis

5) We have moderate evidence to say that the probability of customers shopping online will increase from 53%.

1. What type of error could you have made in this scenario? Write the error in context. Type I error 6. In the following situations, indicate whether our strength of evidence will become stronger or weaker. a. It is announced that the researchers were actually only able to get data on 500 customers in 2015. (Assume the value of the observed sample statistics stays the same). i. The strength of evidence would increase. ii. The strength of evidence would decrease. iii. The strength of evidence would stay the same. iv. Not enough information is given. b. We change our research question to “Has there been any evidence to suggest a change in the proportion of online shoppers?” i. The strength of evidence would increase. ii. The strength of evidence would decrease. iii. The strength of evidence would stay the same. iv. Not enough information is given. c. The researchers announced that they made a mistake, and there were actually 410 customers that were shopping online for daily use products. i. The strength of evidence would increase. ii. The strength of evidence would decrease. iii. The strength of evidence would stay the same. iv. Not enough information is given.

III.

For the plot above, choose the correct answer. a. The distribution is (symmetric/skewed). b. The distribution is ……………. (left/right) skewed. c. (Mean/Median) would be good measure to use in this case. Explain briefly why?

you a

Because it is a resistant measure of center and because it is skewed to the left, it will give better measure of center....