## Statistics Experts Assignments

Statistics Experts Assignments

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9.7 Deﬁne the sampling distribution of the mean.

9.8 Specify three important properties of the sampling distribution of the mean.

9.9 If we took a random sample of 35 subjects from some population, the associated sampling distribution of the mean would have the following properties (true or false).

(a) Shape would approximate a normal curve.

(b) Mean would equal the one sample mean.

(c) Shape would approximate the shape of the population.

(d) Compared to the population variability, the variability would be reduced by a factor equal to the square root of 35.

(e) Mean would equal the population mean.

(f) Variability would equal the population variability.

9.13 Given a sample size of 36, how large does the population standard deviation have to be in order for the standard error to be

(a) 1

(b) 2

(c) 5

(d) 100

9.14

(a) A random sample of size 144 is taken from the local population of grade-school children. Each child estimates the number of hours per week spent watching TV. At this point, what can be said about the sampling distribution?

(b) Assume that a standard deviation, (r, of 8 hours describes the TV estimates for the local population of schoolchildren. At this point, what can be said about the sampling distribution?

(c) Assume that a mean, µ, of 21 hours describes the TV estimates for the local population of schoolchildren. Now what can be said about the sampling distribution?

(d) Roughly speaking, the sample means in the sampling distribution should deviate, on average, about ___ hours from the mean of the sampling distribution and from the mean of the population.

(e) About 95 percent of the sample means in this sampling distribution should be between ___ hours and ___ hours.

10.9 The normal range for a widely-accepted measure of body size, the body mass index (BMI), ranges from 18.5 to 25. Using the mid-range BMI score of 21.75 as the null hypothesized value for the population mean, test this hypothesis at the .01 level of signiﬁcance given a random sample of 30 weight-watcher participants who show a mean BMI 5 22.2 and a standard deviation of 3.1.

10.10 Let’s assume that over the years, a paper and pencil test of anxiety yields a mean score of 35 for all incoming college freshmen. We wish to deter-mine whether the scores of a random sample of 20 new freshmen, with a mean of 30 and a standard deviation of 10, can be viewed as coming from this population. Test at the .05 level of signiﬁcance.

10.11 According to the California Educational Code (http://www.cde.ca.gov/ls/fa/sf/peguidemidhi.asp ), students in grades 7–12 should receive 400 minutes of physical education every 10 school days. A random sample of 48 students has a mean of 385 minutes and a standard deviation of 53 minutes. Test the hypothesis at the .05 level of signiﬁcance that the sampled population satisﬁes the requirement.