In a drug trial, 18 people given a real drug had an average endorphin increase of 8 micrograms (s=5.4). 11 people given a sugar pill had an average increase of 4 micrograms (s=2.4). Assuming equal variances, what is the calculated pooled variance (Sp squared)?
Explanation
This question tests the ability to apply the formula for pooled variance, which is a key component of the t-test for two means when population variances are assumed to be equal, as shown in Example 10.5.
Other questions
What is the primary characteristic that distinguishes independent groups from matched pairs in the context of comparing two samples?
According to the Central Limit Theorem as applied to comparing two independent population means, what is the distribution of the newly created random variable representing the difference between the sample means?
What does Cohen's d measure in the context of hypothesis testing with two samples?
In a study comparing two companies, the calculated Cohen's d is 0.85. According to the standards provided in the text, how would this effect size be classified?
When conducting a hypothesis test for two independent population proportions, what is the pooled proportion (pc) used for?
In a study comparing default rates, a sample of 200 current customers (Area A) had 20 defaults, and a sample of 200 new customers (Area B) had 12 defaults. What is the value of the pooled proportion, pc?
In a hypothesis test for matched or paired samples, the test is fundamentally a:
A study is done to determine if Company A retains its workers longer than Company B. What would be the correct alternative hypothesis (Ha) for this test?
In the Kona Iki Corporation example comparing two shifts, the calculated t-value was found to be in the tail of the t-distribution. What is the correct decision regarding the null hypothesis?
When testing the difference between two means and assuming equal population variances, how does using a pooled sample variance affect the estimate compared to individual sample variances?
What are the five basic assumptions that must be fulfilled to perform a one-way ANOVA test, as listed in the textbook?
The null hypothesis for a one-way ANOVA test is that:
What is the F-ratio in a one-way ANOVA test a ratio of?
In a study of hypnotism's effect on pain, a 'before' score is matched to an 'after' score for each subject. For one subject, the 'before' score was 9.0 and the 'after' score was 7.4. What is the calculated difference for this matched pair?
A study compares the mean height of plants given a special food to plants given no food. The population standard deviations are known. Which test statistic is appropriate?
In a comparison of two floor waxes from Example 10.7, Wax 1 had a sample mean of 3 months and Wax 2 had a sample mean of 2.9 months. The test concluded that there was not sufficient evidence that Wax 1 was more effective. This is because:
When the sum of the sample sizes (n1 + n2) is greater than 30, what approximation can be used for the Student's t-distribution?
In a study comparing grades from a hybrid class and a standard lecture class, the test statistic was calculated to be -0.65. With a 5 percent significance level for a two-tailed test, the critical value is +/- 1.96. What is the correct conclusion?
What is the formula for degrees of freedom (df) in a test of two independent groups with population variances unknown and not assumed to be equal?
When comparing two independent population proportions, the underlying distribution for the random variable X (number of successes) is what?
A study is conducted to see if a new diet lowers cholesterol. Eight subjects have their cholesterol measured before and after the diet. This is an example of what kind of test?
For a test comparing two independent population proportions to be valid, what condition must be met regarding the number of successes and failures?
In a test comparing two means with unknown variances, if the sum of the sample sizes (n1 + n2) is 28, which distribution should be used?
A company wants to know if a new training program is effective. They measure the scores of 20 employees before (mean = 20.4) and after (mean = 23.9) the program. The mean of the differences was 3.5. What is the null hypothesis (H0) for this matched-pairs test?
What is the key term for a weighted average of two variances that can be used when it is assumed the two populations have the same variance?
If two events are independent, the knowledge that one occurred:
The test statistic for comparing two independent population means with known standard deviations follows which distribution?
A softball coach tests the effectiveness of a strength program on 4 players. The mean difference in lift was 21.3 pounds, and the standard deviation of the differences was 46.7 pounds. What is the calculated test statistic (tc)?
If the null hypothesis for a comparison of two population means is H0: µ1 = µ2, what is the value of δ0 (the hypothesized difference)?
When comparing two independent population proportions, how is the standard error of the difference calculated for the test statistic?
What is the primary reason for using a Student's t-test instead of a z-test when comparing two population means?
In the study comparing Democratic and Republican senators' ages in Example 10.8, the p-value was found to be larger than the 5 percent significance level. What does this result imply?
Which of the following scenarios is an example of a test for two independent proportions?
If a hypothesis test comparing two means yields a test statistic that is very close to zero, what is the likely conclusion?
In Example 10.10, eight subjects' pain levels were measured before and after hypnotism. The mean of the differences was -3.13 and the standard deviation of the differences was 2.91. What are the degrees of freedom for this test?
If a researcher assumes two populations have equal variances when they do not, what is a likely consequence for their two-sample t-test?
A test for the difference in the proportion of men and women who prefer a certain brand of coffee is conducted. This is an example of what kind of hypothesis test?
The test statistic for comparing two independent proportions (p'1 - p'2) follows which distribution, according to the Central Limit Theorem?
What does a negative value for the random variable, x̄d = x̄1 - x̄2, indicate in a matched-pairs test?
In a study of two soft drinks, Beverage A had a mean of 36 grams of sugar and Beverage B had 38 grams. The test is to see if Beverage B has more sugar. What is the correct null hypothesis?
Which of the following is NOT an assumption for the F test of two variances?
If the calculated F statistic is much larger than one, what does this suggest about the two population variances?
In a study comparing two professors' exam scores, Professor A had 10 students and Professor B had 10 students. This is an example of:
In the comparison of weighted alpha for banks in the northeast versus the west (Try It 10.5), what is the random variable of interest?
If a one-way ANOVA test results in a very small p-value (e.g., less than 0.05), what is the appropriate conclusion?
A study tests if a software patch reduces system failures. Data is collected on 8 installations 'before' and 'after' the patch. This setup is an example of:
In a study of two independent groups of students, Group A (n=25) has a mean score of 5, and Group B (n=16) has a mean score of 4.7. The test aims to see if the means are different. What is the correct null hypothesis?
What is the primary purpose of calculating the degrees of freedom in a two-sample t-test?
What does a one-way ANOVA test actually use to help determine if the means of several groups are equal?