Statistics Fundamentals GMLE Practice Questions (Page 9)

Questions 41–45

1. 41foundation · easy

   Which of the following is a characteristic of the normal distribution?

   • AIt is symmetric and bell-shaped.
   • BIt is skewed to the right.
   • CIt has two modes.
   • DIt is defined only for non-negative values.
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2. 42application · medium

   A marketing analyst finds a strong positive correlation (r=0.85) between the number of social media ads a customer views and the amount they spend. The analyst concludes that viewing more ads causes higher spending. Which additional analysis would best help evaluate whether this conclusion is justified?

   • ACalculate the p-value for the correlation coefficient.
   • BRun a randomized experiment where customers are randomly assigned to see different numbers of ads.
   • CIncrease the sample size to reduce sampling error.
   • DFit a multiple regression with more demographic variables.
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4. 43application · medium

   A data analyst at a logistics company wants to estimate the average delivery time for a new route. They have delivery times for a random sample of 50 shipments. The sample mean is 4.2 days and the sample standard deviation is 1.1 days. Which interpretation of a 95% confidence interval for the mean delivery time is correct?

   • AIf the sampling process were repeated many times, approximately 95% of the computed intervals would contain the true population mean.
   • BThere is a 95% probability that the true population mean lies within the computed interval.
   • C95% of the delivery times in the sample fall within the computed interval.
   • DThe true population mean is definitely within the interval because the sample was random.
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5. 44application · medium

   A data scientist finds a strong positive correlation (r = 0.9) between ice cream sales and drowning incidents. Which conclusion is most defensible?

   • ADrowning incidents cause people to buy more ice cream.
   • BIce cream sales and drowning incidents are correlated, but a third variable such as warm weather likely drives both.
   • CThe correlation is spurious and should be ignored entirely.
   • DIncreasing ice cream sales causes more drowning incidents.
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6. 45expert · hard

   A spam filter uses a Bayesian classifier. Initially, 20% of emails are spam. The word 'free' appears in 50% of spam emails and 5% of non-spam emails. An email containing 'free' arrives. What is the posterior probability that this email is spam?

   • AApproximately 90%
   • BApproximately 71.4%
   • CApproximately 50%
   • DApproximately 20%
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