Statistical Analysis Assignment 08

Statistical Analysis Assignment 08

1. In the following situations, indicate whether you’d use the normal distribution, the t distribution, or neither.

a. The population is normally distributed, and you know the population standard deviation.b. You don’t know the population standard deviation, and the sample size is 35.c. The sample size is 22, and the population is normally distributed.d. The sample size is 12, and the population is not normally distributed.e. The sample size is 45, and you know the population standard deviation.

Statistical Analysis Assignment 08

2. The prices of used books at a large college bookstore are normally distributed. If a sample of 23 used books from this store has a mean price of $27.50 with a standard deviation of $6.75, use Table 10.1 in your textbook to calculate the following for a 95% confidence level about the population mean. Be sure to show your work.

a. Degrees of freedomb. The critical value of tc. The margin of errord. The confidence interval for a 95% confidence level

3. Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college:

 Play chess

Don’t play chess

Male students

25

162

Female students

19

148

Answer the following questions about the table. Be sure to show any calculations.

a. How many students in total were surveyed?b. How many of the students surveyed play chess? c. What question about the population of students at the state college would this table attempt to answer?d. State Hº  and Hª for the test related to this table.

4. Answer the following questions about an ANOVA analysis involving three samples.

a. In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?b. State the null and alternate hypotheses for a three-sample ANOVA analysis. c. What sample statistics must be known to conduct an ANOVA analysis?d. In an ANOVA test, what does an F test statistic lower than its critical value tell us about the three populations we’re examining?

SAMPLE ANSWER

1. In the following situations, indicate whether you’d use the normal distribution, the distribution, or neither.

1. The population is normally distributed, and you know the population standard deviation.

Since the population is normally distributed and we know the population standard deviation it is a normal distribution (z-distribution).

35. You don’t know the population standard deviation, and the sample size is 35.

We don’t know the population standard deviation, but we know the sample size is 35 we will do a normal, t-distribution.

1. The sample size is 22, and the population is normally distributed.

With a normal distribution and a sample size of 22 we will do a normal, t-distribution.

Statistical Analysis Assignment 08

1. The sample size is 12, and the population is not normally distributed.

Since the population isn’t normal and the sample size is 12 we will do neither distributions.

1. The sample size is 45, and you know the population standard deviation.

Knowing the population standard deviation and the sample size we will do a normal distribution, (z-distribution).

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2. The prices of used books at a large college bookstore are normally distributed. If a sample of 23 used books from this store has a mean price of $27.50 with a standard deviation of $6.75, use Table 10.1 in your textbook to calculate the following for a 95% confidence level about the population mean. Be sure to show your work.

Given:

Sample size: n :23

Sample mean: ̅x : $27.50

Sample Standard deviation: ơ: $6.75

95% Confidence Level

Level of Significance = α = 1-95 = 0.05

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1. Degrees of freedom,

df: n-1 = 23-1 = 22 Degrees of freedom

1. The critical value of t: 1-α/2,

df = 1-0.05/2, 22 = 0.975, 23 = 2.074

1. The margin of error:

z x ơ/ √n = 1.96 x 6.75/√23 = (1.96 x 6.75√23) / 23 = (13.23 √23)/ 23 = $2.758 = $2.76

1. The confidence interval for a 95% confidence level:

 ̅x ± z x ơ / √n =

3. Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college:

Answer the following questions about the table. Be sure to show any calculations.

1. How many students in total were surveyed?

25+19+162+148 = 354

1. How many of the students surveyed play chess? 

25+19 = 44

1. What question about the population of students at the state college would this table attempt to answer?

The population of male students who play chess (p₁) is equal to the population of female students who play chess (p₂).

1. State Hºand Hª for the test related to this table.

Hº: p₁=p₂       Hª: p₁≠p₂

4. Answer the following questions about an ANOVA analysis involving three samples.
5. In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?

What we are trying to determine about the three populations that ANOVA is taken from is the difference in means. It’s a way to figure out if the survey or experiment results are significant.

1. State the null and alternate hypotheses for a three-sample ANOVA analysis.

H0:μ1=μ2=μ3=…

H_a: At least one of the means is different from the others.

1. What sample statistics must be known to conduct an ANOVA analysis?

Sample statistics of the sample size, mean and standard deviations of all comparison groups must be known in order to conduct an ANOVA analysis.

1. In an ANOVA test, what does an F test statistic lower than its critical value tell us about the three populations we’re examining?

When the F test statistic is lower than its critical value this tells us that at least one of the three populations means we are comparing is different. This indicates that the null hypothesis is rejected.

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