Question

In: Math

Using SPSS: You are conducting an experiment to see if growing up bilingual has any effect...

Using SPSS:

You are conducting an experiment to see if growing up bilingual has any effect on a person’s verbal ability later in life. You recruit two groups of subjects: Group 1 consists of native English speakers that speak no other languages. Group 2 consists of people who speak English and at least one other language fluently, and they acquired their second language before the age of 12. Group 1 has 41 subjects, and Group 2 has 37. Verbal ability is measured through a standardized test, that is scored on a scale of 0-100. Each subject is administered the test, and their scores are recorded.

[40 pts] Next, you want to compare the scores of the two groups. You believe that the bilingual subjects (Group 2) will score higher on average than the monolingual subjects (Group 1). Use group1.sav and group2.1.sav for this problem.

What test should you perform here? [5 pts]

What are the distributions of each group? [5 pts]

What are the null/alternative hypotheses? [5 pts]

Run the test in SPSS. [5 pts]

Report your results, as in part 1. [10 pts]

Make a plot comparing the distributions of the two groups. [10 pts]

group1.sav:

84.0781458648940
78.1659813381156
83.2097990726180
74.6179953832211
80.2209401911208
84.9246643735632
79.5972632452217
80.3692891088453
75.5014243441437
76.8739343384229
83.9250985668693
75.3718964391512
78.9411130336794
80.1669903661018
78.2992377573003
78.7896332931477
71.0962392023740
84.1626256134368
82.4740174461893
78.3526586448991
73.3404985790769
83.2337839161124
84.6766160746263
70.7541667161686
83.1011338187307
77.5797973931312
81.3983154504291
78.7066558698611
86.2556403970559
74.8616971481931
81.7496553846257
76.1337325292457
76.4781081018565
79.1532261410977
80.6304842615301
84.1827007993516
80.7528310629980
71.3705246775774
78.5325983274464
78.0476329999499
87.2320045671994

group2.1.sav:

80.8028582039345
92.1782185508421
81.7624767266380
87.6090549775763
81.7988630107953
79.6059009502792
91.0122984144023
79.6806829604419
75.3399990115149
81.3053918211527
82.8035549255071
81.1637179049344
85.3632256665115
86.7573961689029
79.4778738319496
80.9349084875013
81.5921214879792
80.7109217300939
76.3139725547807
82.1414651646484
75.8356344963212
78.0785409762354
81.7487710395530
82.8013055546603
81.0426679680293
85.9590818056062
76.2803153724397
78.6593661496306
80.2492762839822
80.4885216555969
73.6726193385933
85.7176440415797
85.1825156137993
87.8187958603501
79.5842202611197
81.9787940432406
91.0181477610718

Expert Solution

We perform one sided two sample t-test.

Descriptive statistics

Statistics

Variable	N	Mean	StDev	Skewness
group1.sav:	41	79.447	4.118	-0.27
group2.1.sav:	37	82.013	4.362	0.53

from thew skewness coefficient we can say that distributions follow approximately normal with left skew in group-1 and right skew in group2.

Two-Sample T-Test and CI: group1.sav:, group2.1.sav:

Method

μ₁: mean of group1.sav:

µ₂: mean of group2.1.sav:

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
group1.sav:	41	79.45	4.12	0.64
group2.1.sav:	37	82.01	4.36	0.72

Estimation for Difference

Difference	95% Upper Bound for Difference
-2.566	-0.962

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ < 0

T-Value	DF	P-Value
-2.66	74	0.005

since p-value is less than 0.05 we reject null hypothesis and we claim that group2 scores better than group1.

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