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Concept explainers
For Exercises 7 through 31, perform the following steps.
a. State the hypotheses and identify the claim.
b. Find the critical value.
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
28. Fathers in the Delivery Room On average, 79% of American fathers are in the delivery room when their children are born. A physician’s assistant surveyed 300 randomly selected first-time fathers to determine if they had been in the delivery room when their children were born. The results are shown here. At α = 0.05, is there enough evidence to reject the claim that the proportions of those who were in the delivery room at the time of birth are the same?
Source: Daniel Weiss, 100% American.
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Chapter 11 Solutions
Connect Plus Statistics Hosted by ALEKS Access Card 52 Weeks for Elementary Statistics: A Step-By-St
- 9. The concentration function of a random variable X is defined as Qx(h) = sup P(x ≤ X ≤x+h), h>0. Show that, if X and Y are independent random variables, then Qx+y (h) min{Qx(h). Qr (h)).arrow_forward10. Prove that, if (t)=1+0(12) as asf->> O is a characteristic function, then p = 1.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?arrow_forward
- 3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forward1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward
- 1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x≤x≤x+h), h>0. = x (a) Show that Qx+b(h) = Qx(h).arrow_forward
- Suppose that you buy a lottery ticket, and you have to pick six numbers from 1 through 50 (repetitions allowed). Which combination is more likely to win: 13, 48, 17, 22, 6, 39 or 1, 2, 3, 4, 5, 6? barrow_forward2 Make a histogram from this data set of test scores: 72, 79, 81, 80, 63, 62, 89, 99, 50, 78, 87, 97, 55, 69, 97, 87, 88, 99, 76, 78, 65, 77, 88, 90, and 81. Would a pie chart be appropriate for this data? ganizing Quantitative Data: Charts and Graphs 45arrow_forward10 Meteorologists use computer models to predict when and where a hurricane will hit shore. Suppose they predict that hurricane Stat has a 20 percent chance of hitting the East Coast. a. On what info are the meteorologists basing this prediction? b. Why is this prediction harder to make than your chance of getting a head on your next coin toss? U anoiaarrow_forward
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