Section 7.1 Day 3

Quiz when ? no note card terminology & sample distribution

A parameter is __________________.

A parameter is a summary number describing a population.

A statistic is ____________________.

A statistic is a summary number calculated from a sample taken from a population.

A sampling distribution is ______________.

A sampling distribution is the distribution of a sample statistic in repeated random samples of the same fixed size, n.

P5, page 419

P5 (a)

P5 (a) L1 STAT CALC 1: 1-Var Stats

P5 (a) 1- Var Stats x = 261.8 ∑x = 1309 ∑x2 =490351 Sx = 192.1293835

P5(a) 1- Var Stats x = 261.8 population mean ∑x = 1309 ∑x2 =490351 σx = 171.8457448 population standard deviation

P5

P5(c) 1- Var Stats x = 261.8 ∑x = 2618 ∑x2 = 796133.5 Sx = 110.9259513

P5 1- Var Stats x = 261.8 sampling distribution mean ∑x = 2618 σx = 105.2335973 standard error

P5 (c) (c) The mean of the sampling distribution is 261.8, which is exactly the mean of the population. So, the sample mean is an unbiased estimator of the population mean.

P5 (d)  

E5, page 422

E5, page 422

E5, page 422 b. 62, 63, 64, 64, 65 62 and 63 63 and 64 64 and 64 62 and 64 63 and 64 64 and 65 62 and 64 63 and 65 64 and 65 62 and 65

E5, page 422 c. In the same order as the samples listed in part b, their means are 62.5, 63, 63, 63.5, 63.5, 63.5, 64, 64, 64.5, and 64.5.

E5, page 422 The exact sampling distribution of the sample mean for samples of size 2 is shown in this dot plot.

E5, page 422 The sampling distribution has a mean of 63.6 and a standard error of about 0.6245. The population has a mean of 63.6 and a standard deviation of about 1.0198. The two means are exactly the same and, as usual, the standard error is smaller than the standard deviation of the population.

E5, page 422

E5, page 422

P1, p. 418

P1, p. 418

P1

P1

P1, p. 418 1 2 3 4 5 6 7 8 MATH PRB randInt(1, 8) No repeat in sample

P1

P1

P2 (a), Page 418

P2 (a) I is B, which is irregular in shape and has a spread nearly as large as the spread of the population. II is A, which is somewhat mound-shaped with a narrower spread. III is C, which is mound-shaped and has a very narrow spread. All of these distributions have centers very close to the center of the population.

P4, page 419

P4 (a)

P4

P4b (con’t)

P(paid $3 million or more) 12/15

E1

E1, Page 420 a. Histogram A has sample size of 20. Histogram B has sample size of 1. Histogram C has sample size of 2. Histogram D has sample size of 50. As sample size increases, spread decreases.

E1 b. The means all appear to be in the neighborhood of 4.5. Sample size does not appear to affect the mean.

E1 c. The larger the sample size, the smaller the spread.

P6, page 420

P6, page 420 a. The population parameter we are estimating is the population range. Range = max – min = 527 – 56 = 471 mi2

P6

P6

E9, page 423

E9

E9 (con’t)

Questions? Quiz tomorrow