STAT 219 | Week 17 Quiz | Complete Solution

A shipment of small lab mice arrives at an animal care facility with a nominal weight of 10 g per mouse. A sample of five mice is selected and weighed. The average weight of the sample is 10.2 g, and the standard deviation of weight among mice is 2 g. Find a 95% confidence interval for the mean weight of all the mice in the shipment.   
(a) 10 ± 2.48  
(b) 10.2 ± 2.48  
(c) 10 ± 2.30  
(d) 10.2 ± 2.30 
 
A shipment of small lab mice arrives at an animal care facility with a nominal weight of 10 g per mouse. A sample of 10 mice is selected and weighed. The technician wishes to test the hypothesis that the average weight of the mice matches the nominal value vs. that the mice are underweight at  . Here is some computer output on the analysis of this data:    Based on the output above, which of the following is correct?   

(a) Because the 95% confidence interval contains the value 8.77, there is no evidence that the mean weight differs from the nominal weight.  
(b) The standard error of 0.60 g measures the variation in weights of individual mice.  
(c) Ninety-five percent of mice weigh between 7.4 and 10.1 g.
(d) The margin of error is 1.37 g.

 
A shipment of small lab mice arrives at an animal care facility with a nominal weight of 10 g per mouse. A sample of 10 mice is selected and weighed. The technician wishes to test the hypothesis that the average weight of the mice matches the nominal value vs. that the mice are underweight at . Here is some computer output on the analysis of this data:    Which are the null and alternative hypotheses?   
(a)     (b)     (c)     (d)   
 
A shipment of small lab mice arrives at an animal care facility with a nominal weight of 10 g per mouse. A sample of 10 mice is selected and weighed. The technician wishes to test the hypothesis that the average weight of the mice matches the nominal value vs. that the mice are underweight at  . Here is some computer output on the analysis of this data:    Which of the following is correct?   
(a) The p-value is 0.07 and there is no evidence at   that the mean weight is less than the nominal weight.   (b) The p-value is 0.04 and there is evidence at   that the mean weight is less than the nominal weight.   (c) The p-value is 0.96 and there is no evidence at   that the mean weight is less than the nominal weight.   (d) The p-value is 0.05 and there is no evidence at   that the mean weight is less than the nominal weight. 
 
Can rats learn? The following table is the time(s) taken for rats to run a maze twice:
Rat    1    2    3    4
First time    440    600    720    630
Second time    450    520    720    600

Assume that the changes in time (second time - first time) have an approximately Normal distribution. A 90% confidence interval for the mean change in time to run the maze is:   
(a) -25 ± 64.3.   (b) -25 ± 47.5.   (c) -25 ± 43.1.   (d) -25 ± 33.2.
  
Can rats learn? A sample of 10 rats run a maze twice and the times are recorded for each trial. The following is an analysis of the data (first time - second time):    Assume that the changes in times (first time - second time) have an approximate Normal distribution. Which of the following is correct?   
(a) Because the 95% confidence interval for the mean difference includes the value 37, there is no evidence of a difference in mean time between the two trials.  
(b) Because the p-value is 0.0013, there is less than a 1% chance that the times remained the same.  
(c) About 95% of rats would see a decrease in their time by an average of 37 seconds.  
(d) We have strong evidence at   that the mean time in the first trial around is greater than the mean time on the second trial. 
 
Which of the following is correct?   
(a) Matched pairs designs are preferred because they require fewer subjects.  
(b) The matched pairs t test is robust against non-normality as long as the standard deviation of the differences is large.  
(c) Matched pair designs can be used for any data as long as the two sample sizes are equal.  
(d) The matched pairs t test is the same as the one-sample t test but done on the differences. 

 
Which of the following is correct?   
(a) The t procedures can be used with convenience samples as long as the sample size is large.  
(b) The t procedures can be used with an SRS of more than 40 observations even if the data are skewed.  
(c) The t procedures are robust against outliers.  
(d) The t procedures requires that the variable follow a Normal distribution even if the sample size is large. 



Data on the blood cholesterol levels of 34 rats (milligrams per deciliter of blood) give   = 85 and s = 12. A 95% confidence interval for the mean blood cholesterol of rats under this condition is computed. Which of the following would be most worrisome for the validity of the confidence interval?   
(a) the presence of a clear outlier in the raw data  
(b) a mild skew in the stemplot of the raw data  
(c) not knowing the population standard deviation  
(d) the blood cholesterol values do not follow a Normal distribution 
 
Which of these settings does NOT allow use of a matched pairs t procedure?   
(a) You interview both the husband and the wife in 64 married couples and ask each person about their ideal number of children.  
(b) You interview a sample of 64 unmarried male students and another sample of 64 unmarried female students and ask each about their ideal number of children.  
(c) You interview 64 female students in their freshman year and again in their senior year and ask each about their ideal number of children.  
(d) You interview 64 female students and their mothers and ask each about their ideal number of children.