In the following situations, indicate whether you’d use the normal distribution, the t distribution, or neither.
The population is normally distributed, and you know the population standard deviation.
I would use normal distribution (z-distribution) because the population is normally distributed and the standard deviation is known.
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You don’t know the population standard deviation, and the sample size is 35.
I would use t-distribution because the standard deviation is not known and the sample size is small.
The sample size is 22, and the population is normally distributed.
I would use t-distribution since the sample size is small and the population is normally distributed.
The sample size is 12, and the population is not normally distributed.
Neither normal distribution nor t-distribution can be used since the population is not normally distributed and the sample size is small.
The sample size is 45, and you know the population standard deviation.
Normal distribution (z-distribution) because the size of the sample and the standard deviation is known.
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.
From the question, we are given the size of the sample, n, the mean of the sample, x, the standard deviation, σ, and the 95% confidence level.
Degrees of freedom
The critical value of t
The margin of error
The confidence interval for a 95% confidence level
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.
How many students in total were surveyed?
How many of the students surveyed play chess?
What question about the population of students at the state college would this table attempt to answer?
The table is attempting to compare the number of male and female students playing chess at the state college.
State Hº and Hª for the test related to this table.
Answer the following questions about an ANOVA analysis involving three samples.
In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?
In this ANOVA analysis, we are trying to compare the means of three samples and determine if there are any statistically significant differences between the means of these three samples.
State the null and alternate hypotheses for a three-sample ANOVA analysis.
What sample statistics must be known to conduct an ANOVA analysis?
To conduct an ANOVA analysis, the size of the samples, their mean x, as well as, their standard deviation, σ, ought to be known.
In an ANOVA test, what does an F test statistic lower than its critical value tell us about the three populations we’re examining?
The F-statistic determined from the data signifies the variability among the means of the three samples. If the F test is lower than the critical value, it means that the means are not all equal. Therefore, the null hypothesis has to be rejected.
