statistics-correlation

u06a1 – One-Sample t Tests, Independent Samples t Tests, and Confidence Intervals

Complete the following problems within the Word document (do not submit other files). Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. (You may want to highlight your answer or use a different type of color to set it apart.)

Submit the document to your instructor by Sunday, 11:59 p.m. central time.

Problem Set 6.1: One-Sample t Test

Criterion: Hand calculate a one-sample t test.

Data: Rex’s Flower Shop advertised freshly cut roses that last longer than other roses. The mean vase life for a rose is 8 days. The following is a sample of the vase life of 9 bouquets of roses from Rex’s Flower Shop: 8, 6, 12, 11, 8, 9, 14, 15, 10.

Instruction: Complete the following:

a. State the nondirectional hypothesis. H0: Rex flower last longer than other roses.

b. State the critical t for α = .05 (two tails). t(8)=2.306

c. Calculate t. Show your work. Calculate the test statistic. Mean of the 9 bouquets of roses =93/3=10.33. Standard deviation= 2.96

d. Answer: Is the vase life of Rex’s roses significantly different than the population mean? Explain.

Remember, you must show all of your work to receive credit.

Problem Set 6.2: One-Sample t Test in SPSS

Criterion: Calculate a one-sample t test in SPSS.

Data: Use the Rex’s Flower Shop data from problem set 6.1.

Instruction: Complete the following:

a. Enter the data from problem set 6.1 into SPSS and name the variable as Roses.

b. In the Toolbar, click Analyze, select Compare Means, and then select One-Sample t Test.

c. Select Roses, then click Arrow to send it over to the right side of the table. In the box labeled Test Value, enter 8.

d. Click OK and copy and paste the output into the Word document.

e. Compare your SPSS output to your hand calculations from Problem Set 6.1. Are they the same?

Warnings

The One-Sample Test table is not produced.

One-Sample Statistics
	N	Mean	Std. Deviation	Std. Error Mean
Roses	0a,b	.	.	.
a. t cannot be computed because the sum of caseweights is less than or equal 1.
b. t cannot be computed. There are no valid cases for this analysis because all caseweights are not positive.

(Assignment continues on next page.)

Problem Set 6.3: Confidence Intervals

Criterion: Calculate confidence intervals using SPSS.

Data: Use the SPSS output from Problem Set 6.2 above.

Instruction: Based on the SPSS output from Problem Set 6.2, including a test value (population mean) of 8, calculate the 95% confidence interval.

Problem Set 6.4: Standard Error of the Difference Between the Means

Criterion: Analyze the relationship between standard error and the difference between the means.

Data: A researcher examines the results of two separate studies. In the first study, the difference between Group A and Group B is two points, but the standard error is large and the difference is not significant. In the second study, the difference between Group A and Group B is also two points, but the standard error is small and the difference is significant.

Instruction: Answer this: What might be the reason for the difference in the standard error across the two studies? The difference in the standard error can be because of difference in sample size. A larger standard error can be because the sample size used is small, whereas a smaller standard error can be because of a large sample size.

Problem Set 6.5: Independent Samples t Test in SPSS

· Criterion: Calculate an independent samples t test in SPSS.

· Data: Ms Z has two groups of band students. She asks Group 1 to use her new embouchure strengthening cream before practice and asks Group 2 to practice as usual. The groups practiced for the following number of minutes:

· Minutes of practice:

· Group 1: 55, 44, 62, 30, 78, 50, 52.

· Group 2: 31, 40, 53, 22, 41, 16, 33.

· Instruction: Complete the following steps:

a. Open SPSS and create a New Dataset.

b. Click the Variable View tab and type Groups in the Name column. Click on the gray box in the Values column. Value Labels window appears. Enter 1 in the Value area and enter Embouchure Cream in the Label area. Click Add. Now enter 2 in the Value area and enter No Cream in the Label area. Click Add. Click OK. The Variable View screen appears.

c. In row two, enter Minutes in the Name column.

d. Click Data View.

(Assignment continues on next page.)

e. Enter the minutes of practice data (e.g., 1 under Groups and 55 under Minutes; 2 under Groups and 31 under Minutes).

f. In the Toolbar, click Analyze, select Compare Means, and then select Independent-Samples t Test.

g. Select Minutes, then click Arrow to send it over to the Test Variable box.

h. Select Groups and then click Arrow to send it over to the Grouping Variable box.

i. Click Define Groups and enter 1 for Group 1 and enter 2 for Group 2. Click Continue.

j. Click OK and then copy and paste the output to the Word document.

Group Statistics
	GROUPS	N	Mean	Std. Deviation	Std. Error Mean
MINUTES	EMBOUCHURE CREAM	7	53.0000	14.88847	5.62731
	NO CREAM	7	33.7143	12.40584	4.68897

Independent Samples Test
	Levene's Test for Equality of Variances	t-test for Equality of Means
	F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
								Lower	Upper
MINUTES	Equal variances assumed	.038	.849	2.633	12	.022	19.28571	7.32482	3.32629	35.24514
	Equal variances not assumed			2.633	11.622	.022	19.28571	7.32482	3.26848	35.30295

Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
			Lower	Upper
.022	19.28571	7.32482	3.32629	35.24514
.022	19.28571	7.32482	3.26848	35.30295
95% Confidence Interval of the Difference
Lower	Upper
3.32629	35.24514
3.26848	35.30295

Problem Set 6.6: Independent Samples t Test

Criterion: Identify IV, DV, and hypotheses and evaluate the null hypothesis for an independent samples t test.

Data: Use the information from Problem Set 6.5.

Instruction: Complete the following:

a. Identify the IV and DV in the study.

b. State the null hypothesis and the directional (one-tailed) alternative hypothesis.

c. Can you reject the null hypothesis at α = .05? Explain why or why not.