Answer :
Final answer:
The mean age at which infants speak their first word in English is determined through a hypothesis test using the given data. The hypothesis test concludes that there is not enough evidence to suggest that the mean age is greater than 12 months.
Explanation:
The null hypothesis is that the mean age at which infants speak their first word is not greater than 12 months. The alternative hypothesis is that the mean age at which infants speak their first word is greater than 12 months.
To test this hypothesis, we can perform a one-sample t-test. We calculate the sample mean of the given data, which is 12.55 months, and the standard deviation of the sample, which is 4.86 months. Using these values, we can calculate the t-statistic, which is approximately 0.30. The p-value corresponding to this t-statistic is approximately 0.384, which is greater than the significance level of 0.05.
Therefore, based on the test, we cannot reject the null hypothesis. There is not enough evidence to suggest that the mean age at which infants speak their first word is greater than 12 months.