Question

In: Statistics and Probability

. Independent samples t-test:    You want to test whether plants grow better when you talk...

. Independent samples t-test:   

You want to test whether plants grow better when you talk to them. You obtain two sets of philodendrons, talk to one set and ignore the other (except to water them). After 6 months, you measure their growth in inches. The data are below. Conduct an independent samples t-test with alpha = .05 with a nondirectional test to determine if there was a significant difference between the two sets of plants.

Answer the following questions. You can use SPSS for this problem, but if you do this “by hand” be sure to show your work.

  1.       What are the null & alternative hypotheses?
  2.       What are the degrees of freedom?
  3.       What is the critical value of t?
  4.       What is the observed value of t?
  5.       What is your decision about the null hypothesis/why?
  6.        If appropriate, calculate Cohen’s d and report its value.
  7.       Write the t statistic using appropriate APA style.
  8.       How would you interpret your findings?    

          Not talked to                         Talked to

                   4                               8

                   2                               7

                   8                               13

                   4                               6

                   6                               5

                   6                               11

                   3                               8

                   5                               9  

                   6                               10

Solutions

Expert Solution

a)

Ho :   µ1 =  µ2
Ha :   µ1 ╪ µ2  

b)  Degree of freedom, DF=   n1+n2-2 =    16

c) critical t value =   ± 2.120 (excel formula =t.inv(α/2,df)

d)

Sample #1   ---->   1                  
mean of sample 1,    x̅1=   4.89                  
standard deviation of sample 1,   s1 =    1.83                  
size of sample 1,    n1=   9                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   8.56                  
standard deviation of sample 2,   s2 =    2.51                  
size of sample 2,    n2=   9                  
                          
difference in sample means =    x̅1-x̅2 =    4.8889   -   8.6   =   -3.67  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    2.1953                  
std error , SE =    Sp*√(1/n1+1/n2) =    1.0349                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -3.6667   -   0   ) /    1.03   =   -3.5431

e) Decision:   | t-stat | > | critical value |, so, Reject Ho  
f)

effect size,      
cohen's d =    |( x̅1-x̅2 )/Sp | =    1.6702

g) t(16) = -3.54 , reject the null hypothesis

h) There is enough evidence of significant difference


Related Solutions

Independent Samples t-test in SPSS Imagine that you want to determine whether people who are homeless...
Independent Samples t-test in SPSS Imagine that you want to determine whether people who are homeless have greater levels of depression lf they HAVE A DISABILITY compared to people who are homeless and DO NOT have a disability. The scores below represent the raw scores for the Stewart Depression Scale, which measures people's level of depression {higher scores represent greater depression levels). You will need to take the raw scores from the table below, and compute at-test analysis in SPSS....
29. You conducted an independent samples t-test to determine whether there is a difference in productivity...
29. You conducted an independent samples t-test to determine whether there is a difference in productivity between employees who work 5-days per week versus 4-days per week. You find the average units produced for the 5-day work week is 26.6 and the average units produced for the 4-day work week is 24.4. Your standard error (of the differences) is 1.48. Using degrees of freedom of 18 and an alpha of .05, construct a 95% confidence interval. (1 point)
Indicate which test (dependent samples t-test, independent samples t-test, independent samples z-test) is most appropriate for...
Indicate which test (dependent samples t-test, independent samples t-test, independent samples z-test) is most appropriate for the following situation: i. Comparison of mean recycling participation between 9 large cities and 11 small cities ii. Comparison of the weights of 16 Toronto Maple Leaf rookies at the beginning versus the end of the regular NHL season. iii. Comparison of fin length of 35 male and 37 female brook trout sampled in Spruce Lake, Nottingham Forest. iv. Comparison of the mass of...
The Independent Samples t-Test compares the means of two independent groups to determine whether there is...
The Independent Samples t-Test compares the means of two independent groups to determine whether there is statistical evidence that the associated population means are significantly different. The Independent Samples t-Test is a parametric test. Give an example of two variables you would compare, what your theory is and the hypothesis, and how you would find the independent samples t-test in SPSS.
Assignment #3: Independent Samples T test Conduct an Independent Samples T test to answer the questions...
Assignment #3: Independent Samples T test Conduct an Independent Samples T test to answer the questions based on the following scenario. (Assume a non-directional research hypothesis (two-tailed test) and a level of significance of .05) The superintendent who collected data for Assignments 1 and 2, continued to examine the district’s data. One question that concerned the superintendent’s constituencies was the difference between the school performance scores of the superintendent’s district and a neighboring district that had similar demographic and socio-economic...
Assignment #3: Independent Samples T test Conduct an Independent Samples T test to answer the questions...
Assignment #3: Independent Samples T test Conduct an Independent Samples T test to answer the questions based on the following scenario. (Assume a non-directional research hypothesis (two-tailed test) and a level of significance of .05) The superintendent who collected data for Assignments 1 and 2, continued to examine the district’s data. One question that concerned the superintendent’s constituencies was the difference between the school performance scores of the superintendent’s district and a neighboring district that had similar demographic and socio-economic...
2.2. Indicate which test (paired samples (ie dependent) t-test, independent two samples t-test, one-sample t-test, independent...
2.2. Indicate which test (paired samples (ie dependent) t-test, independent two samples t-test, one-sample t-test, independent samples z-test) is most appropriate for the following situations : A. Comparison of weight gain of two groups of 18 cows where one group was raised following standard practices and the other group was raised following “organic” standards. B. Comparison of scores on a fitness test of Olympic-class distance runners (n=20) with the national average score of people of a similar age range (22-31...
1. Identify which test the scenario will use: independent samples t test, paired samples t test,...
1. Identify which test the scenario will use: independent samples t test, paired samples t test, chi square test for goodness of fit, chi square test for independence or chi square test for homogeneity. A. A researcher goes to the parking lot at a large grocery chain and observes whether each person is male or female and whether they return the cart to the correct spot before Chi leaving (yes or no). B. Amber Sanchez, a statistics student, collected data...
Independent Samples T-Test by Group (receiving intervention vs. control group on waiting list) Independent Samples T-Test...
Independent Samples T-Test by Group (receiving intervention vs. control group on waiting list) Independent Samples T-Test t df p Uscreen -7.495 98 < .001 Note. Student's t-test. Independent Samples T-Test by Race (White vs. Black/Hispanic) Independent Samples T-Test t df p Uscreen -2.473 98 0.015 Note. Student's t-test. Independent Samples T-Test by Age (21-24 vs 25-30) Independent Samples T-Test t df p Uscreen 1.478 98 0.143 ᵃ Note. Student's t-test. ᵃ Levene's test is significant (p < .05), suggesting a...
1. For the following experimental designs, indicate whether independent-samples or paired-samples t-test is appropriate: a) Weight...
1. For the following experimental designs, indicate whether independent-samples or paired-samples t-test is appropriate: a) Weight is obtained for each subject before and after Dr. Nogani's new treatment. The hypothesis to be tested is that the treatment has no effect on weight loss. b) Elephants are randomly selected from a jungle and Trunkgrol is administered to one group of elephants and Trunkgro2 to the other. The hypothesis to be tested is that both agents are equally effective in promoting trunk...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT