Solve the following problems.

z-test one sample mean

I. Fortv eiqht 7-year old children who were reading at below grade level asked to read a passage aloud. The number of corrections and omissions were noted. The sample mean number of corrections and omissions was 17.86 with standard deviation of 4.2. If the population mean is 19.9, does the data provide sufficient evidence that the mean number of corrections and omissions for children who are reading below grade level is different from 19.9? Carry out a test using a significance level of 0.01.

t-test one sample mean

2. The paper "Distinguishing the Dimensions of Valence and Belief Consistency in Depressive and Nendepressjye Information Processing" reported that the mean and standard deviation of scores on a self- image scale for 13 clinically depressed women were 28.63 and 13.61 respectively. Suppose that the mean score for depressed women is 28. Test the hypothesis whether the mean sore differs from 28 at 0.05 level of signiflcance.

z-test two sample mean

3. Leucocyte (white blood cell) counts in horses have recently been studied as a possible aid to the diagnosis of respiratory viral infections. The accompanying data on neutrophils the most numerous kind of leucocyte) was reported in a comparative study of counts in horses of different ages.

Age Sample Sample Standard

Size Mean Deviation

2-year-olds 197 51 5.6

4-year-olds 77 56 4.3

Does the data suggest that the true average neutrophil count for 4-year olds exceeds that for 2-year-olds? Carry out a test of using 0.05 level of significance.

t-test two sample mean

4. The mean lifetime of 20 randomly selected bulbs produced by Company A was 14,000 hours with standard deviation of 500 hours, while 25 randomly selected bulbs produced by Company B showed a mean lifetime span of 12,000 hours, with standard deviation of 400 hours. Test whether bulbs produced by company A are similar to those produced by Company B at the 0.01 level of significance.