Question

Use R-Studio to plot this PAIRED SAMPLES T-TEST

A neuroscientist believes that the lateral hypothalamus is involved in eating behavior. If so, then electrical stimulation of that area might affect the amount eaten. To test this possibility, chronic indwelling electrodes are implanted in 10 rats. Each rat has two electrodes: one implanted in the lateral hypothalamus and the other in an area where electrical stimulation is known to have no effect. After the animals have recovered from surgery, they each receive 30 minutes of electrical stimulation to each brain area, and the amount of food eaten during the stimulation is measured. The amount of food in grams that was eaten during stimulation is shown in Table

Subject	1	2	3	4	5	6	7	8	9	10
Lateral hypothalamus	10	18	16	22	14	25	17	22	12	21
Neural area	6	8	11	14	10	20	10	18	14	13

Answer 1

Objective: To test the claim that lateral hypothalamus is involved in eating behaviour. In order to test this claim, we may compare the amount of food eaten during the stimulation in two areas - Lateral hypothalamus and Neural Area, where the electrodes are implanted. If the claim were indeed true, the difference in the amount of food eaten when the impulse given to the two areas - Lateral hypothalamus would be significantly different from Neural Area, where, electrical stimulation is known to have no effect.

To test: $H_{0}:\mu_{d}=0$ Vs   $H_{a}:\mu_{d}\neq 0$ at say, 5% level of significance.

Using R studio:

Untitled1* X Run Source Source on Save 1 #Data 2 LatHy=C(10,18,16,22,14,25,17,22,12,21) 3 Neua=c(6,8,11,14,10,20,10,18,14,13) 4 #Running Paired t test 5 Paired_t_test<-t.test(Lathy, Neua, paired=TRUE) 6 Paired_t_test 7 8 9 7:1 (Top Level) R Script Console > LatHy=C(10,18,16,22,14,25,17,22,12,21) > NeuA=c(6,8,11,14,10,20,10,18,14,13) > Paired_t_test<-t.test(Lathy, Neua, paired=TRUE) > Paired_t_test Paired t-test data: Lathy and Neua t = 5.0765, df = 9, p-value = 0.000666 alternative hypothesis: true difference in means is not equal to o 95 percent confidence interval: 2.938239 7.661761 sample estimates: mean of the differences 5.3 > |

We find that the test is significant (t = 5.0765, p-value = 0.0006 < 0.05) at 5% level. We may conclude that the data provides sufficient evidence to support the claim that the lateral hypothalamus is involved in eating behaviour.

**To be more specific, if we wish to test

To test: $H_{0}:\mu_{d}=0$ Vs   $H_{a}:\mu_{d}> 0$ at say, 5% level of significance.

Untitled1* X Source on Save Run Source #Data 1 2 3 4 5 6 7 8 9 LatHy=C(10,18,16,22,14,25,17,22,12,21) Neua=c(6,8,11,14,10,20,10,18,14,13) #Running Paired t testi Paired_t_test<-t.test(Lathy, Neua, paired=TRUE, alternative="greater") Paired_t_test 4:23 (Top Level) R Script Console > #Data > LatHy=C(10,18,16,22,14,25,17,22,12,21) > NeuA=C(6,8,11,14,10,20,10,18,14,13) > #Running Paired t test Paired_t_test<-t.test(Lathy, Neua, paired=TRUE, alternative="greater") > Paired_t_test Paired t-test data: Lathy and Neua t = 5.0765, df = 9, p-value = 0.000333 alternative hypothesis: true difference in means is greater than 0 95 per cent confidence interval: 3. 386174 Inf sample estimates: mean of the differences 5.3

We find that the test is significant (t = 5.0765, p-value = 0.0003 < 0.05) at 5% level. We may conclude that the data provides sufficient evidence to support the claim that the lateral hypothalamus is involved in eating behaviour.