The research examining the effects of preschool childcare has found that children who spent time in day care perform better on math and language tests than children who stay home with their mothers. The results show that a sample of n = 25 children who attended day care before starting school had an average score of M = 87 with SS = 1536 on standardized math test for which the population mean is μ = 81. The population distribution is normal. Use α = .01.    a. Is this sample sufficient to conclude that the children with a history of preschool day care are significantly better from the general population?   b. Compute the 95% confidence interval.

Two separate samples, each with 16 individuals, receive two different treatments. After treatment, the first sample has SS = 1540 and the second has SS = 1460. If the sample mean difference is 10 points (i.e., M1 -  M2 = 10), compute the t-statistic.   If it is a decimal number, include the numbers after the decimal point. If it is a decimal number with two or more than two places, leave only two decimal places after the decimal point. Please do not round. The t-statistic is

A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. She randomly selected 54 men and 70 women to participate in the study. Each subject was required to step up and down a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained. Two sample T for Men vs Women N Mean StDev SE Mean Men Women 98% CI for mu Men - mu Women (- 12.20, - 1.00) T-Test mu Men = mu Women (vs H2 O C. Ho: H1 = H2; Ha: H1 #H2 (b) Identify the P-value and state the researcher's conclusion if the level of significance was a = 0.01. What is the P-value? P-value =

Women are recommended to consume 1720 calories per day. You suspect that the average calorie intake is different for women at your college. The data for the 12 women who participated in the study is shown below: 1837, 1618, 1820, 1846, 1640, 1700, 1655, 1473, 1563, 1840, 1796, 1854 Assuming that the distribution is normal, what can be concluded at the αα = 0.10 level of significance? For this study, we should use Select an answer z-test for a population proportion t-test for a population mean  The null and alternative hypotheses would be:       H0:H0:  ? μ p  Select an answer > < ≠ =        H1:H1:  ? p μ  Select an answer ≠ = < >    The test statistic ? t z  = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤  αα Based on this, we should Select an answer reject accept fail to reject the null hypothesis. Thus, the final conclusion is that ... The data suggest that the population mean…