Question

Developmental psychologists investigated the effect of high levels of curiosity in early childhood, on intelligence later in life. The local population of 3-year-olds was screened via a test battery assessing curiosity. Twelve of the 3-year-olds scoring in the upper 90% of this variable were given an IQ test at age 3 and again at age 15.

Answer the questions below using α =0.05_2tail.

Participant	IQ-age 3	IQ-age 15
1	100	114
2	105	116
3	125	139
4	140	151
5	108	116
6	122	119
7	117	131
8	112	132
9	135	148
10	128	139
11	104	122
12	98	113

1. What is the alternative hypothesis?                               ["High levels of curiosity in early childhood effects intelligence later in life", "High levels of curiosity in early childhood does not effect intelligence later in life", "High levels of curiosity in early childhood increases intelligence later in life", "High levels of curiosity in early childhood decreases intelligence later in life"]      

2. What is the null hypothesis?                               ["High levels of curiosity in early childhood effects intelligence later in life", "High levels of curiosity in early childhood does not effect intelligence later in life", "High levels of curiosity in early childhood increases intelligence later in life", "High levels of curiosity in early childhood decreases intelligence later in life"]      

3. What inferential test is being conducted?                               ["single sample z test", "single sample t test", "independent group t test", "paired group t test"]      

4. What is the obtained statistic?                               ["7.309", "-5.75", "2.89", "5.75"]      

5. What is the critical value?                               ["2.201", "1.796", "2.064", "1.711"]      

6. What is your decision?                               ["reject the null hypothesis", "retain the null hypothesis", "reject the alternative hypothesis", "accept the null hypothesis", "accept the alternative hypothesis"]      

7. What is your conclusion?                               ["We conclude that high levels of curiosity in early childhood effects intelligence later in life", "We conclude that high levels of curiosity in early childhood does not effect intelligence later in life", "We conclude that high levels of curiosity in early childhood improves intelligence later in life", "We conclude that high levels of curiosity in early childhood decreases intelligence later in life"]      

8. What is your effect size?                               ["large", "medium", "small", "Not applicable as we failed to reject the null hypothesis"]      

9. What error might you be making?

Answer 1

1. What is the alternative hypothesis?  

Ha:μD​ ≠ 0

ie High levels of curiosity in early childhood effects intelligence later in life

2. What is the null hypothesis?  

Ho:μD​ = 0

ie High levels of curiosity in early childhood does not effect intelligence later in life

3. What inferential test is being conducted?   

paired group t test (since it is an IQ test of same sample of size=12 at age 3 and again at age 15)

4. What is the obtained statistic?

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	100	114	-14
	105	116	-11
	125	139	-14
	140	151	-11
	108	116	-8
	122	119	3
	117	131	-14
	112	132	-20
	135	148	-13
	128	139	-11
	104	122	-18
	98	113	-15
Average	116.167	128.333	-12.167
St. Dev.	13.895	13.553	5.766
n	12	12	12

From the sample data, it is found that the corresponding sample means are:

Also, the provided sample standard deviations are:

and the sample size is n = 12. For the score differences we have

The t-statistic is computed as shown in the following formula:

|t|=7.309

Hence,7.309

5. What is the critical value?   

the significance level is α=0.05, and the degrees of freedom are df = 11

Hence, it is found that the critical value for this two-tailed test is tc​=2.201

Hence,2.201

6. What is your decision?

Since it is observed that ∣t∣=7.31>tc​=2.201, it is then concluded that the null hypothesis is rejected.

hence,reject the null hypothesis

7. What is your conclusion?

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1​ is different than μ2​, at the 0.05 significance level.

Hence, We conclude that high levels of curiosity in early childhood effects intelligence later in life.

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