Question: A psychologist claims that the mean age at which children start walking is 12.5 months. Carol believes that the mean age at which children start to walk is greater than 12.5 months. She took a random sample of 20 children and found that the mean age at which these children started walking was 12.9 months. Assume that the population standard deviation is 0.90 months. She wishes to determine if for this study there is statistically significant evidence that the population mean age at which children start walking is greater than 12.5 months.

(a) Write the appropriate null and alternative hypothesis

(b) Compute the value of the z-test statistic. Sketch the distribution of the test statistics and shade the region that corresponds to the p-value

(c) Compute the p-value

(d) Is there statistically significant evidence at the \(\alpha =0.05\) level that the population mean age at which children start walking is greater than 12.5 months?