Statistical Inference in BabiesIs statistical inference intuitive to babies? In other words, are babies able to generalize from sample to population? In this study,1 8-month-old infants watched someone draw a sample of five balls from an opaque box. Each sample consisted of four balls of one color (red or white) and one ball of the other color. After observing the sample, the side of the box was lifted so the infants could see all of the balls inside (the population). Some boxes had an “expected” population, with balls in the same color proportions as the sample, while other boxes had an “unexpected” population, with balls in the opposite color proportion from the sample. Babies looked at the unexpected populations for an average of 9.9 seconds (sd = 4.5 seconds) and the expected populations for an average of 7.5 seconds (sd = 4.2 seconds). The sample size in each group was 20, and you may assume the data in each group are reasonably normally distributed. Is this convincing evidence that babies look longer at the unexpected population, suggesting that they make inferences about the population from the sample?Let group 1 and group 2 be the time spent looking at the unexpected and expected populations, respectively.1Data approximated from Xu, F., and Garcia, V. (2008). “Intuitive statistics by 8-month-old infants,” Proceedings on the National Academy of Sciences, 105(13): 5012-5015, doi: 10.1073/pnas.0704450105. (a) State the null and alternative hypotheses. Your answer should be an expression composed of symbols (b)Calculate the relevant sample statistic.Enter the exact answer. Sample statistic = (c)Calculate the t-statistic.Round your answer to two decimal places.t-statistic = (d)Find the p-value.Round your answer to three decimal places.p-value =

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Statistical Inference in Babies

Is statistical inference intuitive to babies? In other words, are babies able to generalize from sample to population? In this study,¹ 8-month-old infants watched someone draw a sample of five balls from an opaque box. Each sample consisted of four balls of one color (red or white) and one ball of the other color. After observing the sample, the side of the box was lifted so the infants could see all of the balls inside (the population). Some boxes had an “expected” population, with balls in the same color proportions as the sample, while other boxes had an “unexpected” population, with balls in the opposite color proportion from the sample. Babies looked at the unexpected populations for an average of 9.9 seconds (sd = 4.5 seconds) and the expected populations for an average of 7.5 seconds (sd = 4.2 seconds). The sample size in each group was 20, and you may assume the data in each group are reasonably normally distributed. Is this convincing evidence that babies look longer at the unexpected population, suggesting that they make inferences about the population from the sample?

Let group 1 and group 2 be the time spent looking at the unexpected and expected populations, respectively.

¹Data approximated from Xu, F., and Garcia, V. (2008). “Intuitive statistics by 8-month-old infants,” Proceedings on the National Academy of Sciences, 105(13): 5012-5015, doi: 10.1073/pnas.0704450105.

(a) State the null and alternative hypotheses. Your answer should be an expression composed of symbols

(b)Calculate the relevant sample statistic.

Enter the exact answer.

Sample statistic =

(c)Calculate the t-statistic.

Round your answer to two decimal places.

t-statistic =

(d)Find the p-value.

Round your answer to three decimal places.

p-value =

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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