STAT1008 Study Guide - Final Guide: Type I And Type Ii Errors, Confidence Interval, Null Hypothesis

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Events a and b are independent if : p(a if b) = p(a, p(a and b) = p(a)p(b) Binomial probability: (cid:1876) =(cid:1840)(cid:4666) ,(cid:1845)(cid:1831)(cid:4667) (cid:2870)= (cid:1866)(cid:1868)(cid:4666)(cid:883) (cid:1868)(cid:4667) (cid:2870) = (cid:4666)(cid:1876) (cid:4667)(cid:2870) (cid:1868)(cid:4666)(cid:1876)(cid:4667) (cid:1845)(cid:1830)= (cid:4666)(cid:2870)(cid:4667) Type ii error: failing to reject a false h0. Note: if you are testing if something is greater than. To test h0: = 0, ha: 0 (or a one tailed alternative) (cid:1872)= (cid:1845)(cid:1853)(cid:1865)(cid:1868)(cid:1864)(cid:1857) (cid:1871)(cid:1872)(cid:1853)(cid:1872)(cid:1871)(cid:1872)(cid:1855) (cid:1840)(cid:1873)(cid:1864)(cid:1864) (cid:1868)(cid:1853)(cid:1870)(cid:1853)(cid:1865)(cid:1857)(cid:1872)(cid:1857)(cid:1870) (cid:1845)(cid:1831) To find a p-value use a t-distribution with n-2 degrees of freedom. F-statistic: ratio of two values that should be roughly equal under null hypothesis, to reject null hypothesis it should be high. Eliminating any variable (even insignificant ones) will cause r2 to decrease. Can be provided as standard error along with r2. (cid:2869) (cid:1871)- standard deviation or the sample values of the predictor. Confidence interval and prediction interval of a model: Ci (if the question mentions average) and pi for individual.

Related Questions

1. A sample of size n=49 is drawn from a population whose standard deviation is .

(a) Find the margin of error for a 95%confidence interval for .

b) If the sample size were n=60, would the margin of error be larger would be larger or smaller.

2. Determine the point estimate of the population mean and margin of error for the confidence interval. The lower bound is 23; the upper bound is 27. The point estimate of the population mean is? The margin of error for the confidence interval is?

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The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season

x	P(x)
0	0.167
1	0.3289
2	0.2801
3	0.149
4	0.0382
5	0.0368

The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated?

a.Compute the theoretical mean of the random variable X for the given probability distribution.

Meu = ?

b. Compute the theoretical standard deviation of the random variable X for the given probability distribution.

Sigma =?

c.Approximate the mean of the random variable X based on the simulation for 25 games.

Xbar=?

d. Approximate the standard deviation of the random variable X based on the simulation for 25 games.

S=?

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season x P(x) 0 0.167 1 0.3289 2 0.2801 3 0.149 4 0.0382 5 0.0368 The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated? a.Compute the theoretical mean of the random variable X for the given probability distribution. Meu = ? b. Compute the theoretical standard deviation of the random variable X for the given probability distribution. Sigma =? c.Approximate the mean of the random variable X based on the simulation for 25 games. Xbar=? d. Approximate the standard deviation of the random variable X based on the simulation for 25 games. S=?

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6. As the test statistic becomes larger, the p-value

(a) gets smaller

(b) becomes larger

(d) becomes negative.

7. To describe the sampling distribution of the sample proportion, we use

(a) The sample proportion

(b) The population proportion

(d) The population mean

8. When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown and the original distribution is normal:

(a) There always will be a large amount of sampling error.

(b) the t-distribution must be used to obtain the critical value.

(d) the z distribution must be used to obtain the critical value.

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STAT1008 Study Guide - Final Guide: Type I And Type Ii Errors, Confidence Interval, Null Hypothesis

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