Developmental psychology researchers have shown a genetic influence of shyness in infants where infants who were adopted were more likely to be rated as shy at 2 years of age if their biological mothers rated themselves as also being shy (Daniels & Plomin, 1985). A researcher wanted to find out if this finding extended to shyness in identical twins. The researcher recruited a sample of 35 pairs of infants who were identical twins. The researcher asked the infants’ primary caregiver to rate each infant’s level of shyness and compared the shyness level between each identical twin to see if there was a mean difference in shyness between the pairs of identical twins.Daniels, D., & Plomin, R. (1985). Origins of individual differences in infant shyness. Developmental Psychology, 21, 118–121.If μ1 and μ2 represent the shyness rating of the first-born twin and second-born twin, respectively, and let μd be the mean of the differences in the shyness rating (shyness rating of first born − shyness rating of second born) of all identical twins.Which of the following are the appropriate null and alternative hypotheses?H0: μd = 0Ha: μd > 0H0: μd = 0Ha: μd ≠ 0H0: μd ≠ 0Ha: μd = 0H0: μ1 − μ2 = 0Ha: μ1 − μ2 ≠ 0
Question
Developmental psychology researchers have shown a genetic influence of shyness in infants where infants who were adopted were more likely to be rated as shy at 2 years of age if their biological mothers rated themselves as also being shy (Daniels & Plomin, 1985). A researcher wanted to find out if this finding extended to shyness in identical twins. The researcher recruited a sample of 35 pairs of infants who were identical twins. The researcher asked the infants’ primary caregiver to rate each infant’s level of shyness and compared the shyness level between each identical twin to see if there was a mean difference in shyness between the pairs of identical twins.Daniels, D., & Plomin, R. (1985). Origins of individual differences in infant shyness. Developmental Psychology, 21, 118–121.If μ1 and μ2 represent the shyness rating of the first-born twin and second-born twin, respectively, and let μd be the mean of the differences in the shyness rating (shyness rating of first born − shyness rating of second born) of all identical twins.Which of the following are the appropriate null and alternative hypotheses?H0: μd = 0Ha: μd > 0H0: μd = 0Ha: μd ≠ 0H0: μd ≠ 0Ha: μd = 0H0: μ1 − μ2 = 0Ha: μ1 − μ2 ≠ 0
Solution
The appropriate null and alternative hypotheses for this study would be:
H0: μd = 0 Ha: μd ≠ 0
The null hypothesis (H0) is that there is no difference in the mean shyness rating between the first-born twin and the second-born twin (μd = 0). The alternative hypothesis (Ha) is that there is a difference in the mean shyness rating between the first-born twin and the second-born twin (μd ≠ 0). This is because the researcher is interested in whether there is any difference at all, not specifically whether one is greater than the other.
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