2 Sample Tests of Significance
What does the 1 Sample Test of Significance do?
Compares the difference of a sample statistic from one sample with the parameter of a population
For a one sample confidence interval the middle value of any interval is...
The sample statistic or point estimate
2 Sample Confidence Interval for means does what?
It compares two means or checks if there is a difference between two sample means.
What is the formula for a Chi Square Test?
(Observed - Expected)^2 / Expected
What is required for the assumptions of a two sample t test when n is greater than 15 but less than 40?
the distributions of the variable of interest are normal
When would you use a t-test?
σ is unknown
What is the formula for a 1 sample confidence interval of proportions?
p-hat plus or minus z * square root of (p-hat x 1-p-hat/n)
A pollster wants to look at the proportion of high-income voters who support a decrease in the capital gains tax. If the answer must be known to within 0.02 at the 95% confidence level, what size sample should be taken?
The sample must be at least 2401 people.
What is the formula for degrees of freedom for a Goodness of Fit test?
(Number of categories) - 1
What conditions are required in order to perform a two sample t test and how do you check them?
Random-random samples or assignment
Normal -n bigger than or equal to 30 or no outliers and skew in graph
Independent-10% condition or observations are independent of one another
A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score at least 70 on the test. The six students get scores of 62, 92, 75, 68, 83, and 95. Can the professor be at least 90 percent certain that the mean score for the class on the test would be at least 70? Is this a one tailed test? Write the hypothesis and alternative hypothesis.
It is one tailed H0: μ = 70 H a: μ > 70
What is standard error?
The standard error is the estimated standard deviation of a statistic
The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a variance of 0.16 m. Determine the interval of 95% confidence for the average heights of the population.
n = 400 x = 1.75 σ = 0.4 1 − α = 0.95 zα/2 = 1.96 (1.75 ± 1.96 · 0.4/20 ) → (1.7108,1.7892)
What is the purpose of a Chi Square Test?
To see if there if observe counts are close to what is expected.
The amount of a certain trace element in blood is known to vary with a standard deviation of 14.1 ppm (parts per million) for male blood donors and 9.5 ppm for female donors. Random samples of 75 male and 50 female donors yield concentration means of 28 and 33 ppm, respectively. What is the likelihood that the population means of concentrations of the element are the same for men and women? Is this a one tailed or two tailed test? Write the Hypothesis and Alternative Hypothesis.
Two Tailed H0: μ1 = μ2 or H0: μ1 – μ2 = 0 Ha: μ1 − μ2 or: Ha: μ1 − μ2 ≠ 0
A herd of 1,500 steers was fed a special high-protein grain for a month. A random sample of 29 were weighed and had gained an average of 6.7 pounds. If the standard deviation of weight gain for the entire herd is 7.1, what is the likelihood that the average weight gain per steer for the month was at least 5 pounds? Is this a one tailed test or two tailed? Write the Hypothesis and Alternative Hypothesis
One Tailed H0:μ =5 H0:μ > 5
Which of the following statements is true. I. The standard error is computed solely from sample attributes. II. The standard deviation is computed solely from sample attributes. III. The standard error is a measure of central tendency. (A) I only (B) II only (C) III only (D) All of the above. (E) None of the above.
The correct answer is (A)
What happens to the width of the intervals when you increase your sample size?
The intervals become narrower
The p-value of a chi-square test is (0.0003). Write a conclusion using this p-value at the .05 significance level.
Since the P-value (0.0003) is less than the significance level (0.05), we cannot accept the null hypothesis.
An experiment is conducted to determine whether intensive tutoring (covering a great deal of material in a fixed amount of time) is more effective than paced tutoring (covering less material in the same amount of time). Two randomly chosen groups are tutored separately and then administered proficiency tests. Is this one tailed or two tailed? Write the Hypothesis and Alternative
One Tailed H0: μ1 = μ2 or H0: μ1 − μ2 = 0 Ha: μ1 > μ2 or: Ha: μ1 − μ2 > 0
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random in which his team scored 5 9, 4, 11, and 8 runs. Is it likely that his team's scores could have come from the national distribution? Assume an alpha level of .05. Is this one tailed or two tailed? Write the Hypothesis and Alternative Hypothesis
Two Tailed H0: μ = 5.7 Ha: μ ≠ 5.7
Suppose we want to estimate the average weight of an adult male in Dekalb County, Georgia. We draw a random sample of 1,000 men from a population of 1,000,000 men and weigh them. We find that the average man in our sample weighs 180 pounds, and the standard deviation of the sample is 30 pounds. What is the 95% confidence interval. (A) 180 + 1.86 (B) 180 + 3.0 (C) 180 + 5.88 (D) 180 + 30 (E) None of the above
The correct answer is (A)
Suppose that you want to find out the average weight of all players on the football team at Landers College. You are able to select ten players at random and weigh them. The mean weight of the sample of players is 198, so that number is your point estimate. The population standard deviation is σ = 11.50. What is a 90 percent confidence interval for the population weight, if you presume the players' weights are normally distributed? Interpret it.
You are 90 percent certain that the true population mean of football player weights is between 192 and 204 pounds.
What are all the requirements to perform a Chi-Square Test?
1. All expected counts are at least 5
2. Sample is random
3. Independent Condition (10% condition)