A school administrator wants to compare two reading methods: Method S and method

Question

A school administrator wants to compare two reading methods: Method S and method B. A class of 44 students is randomly divided into two groups of 22 each. One is taught with method S and the other is taught with B. Is the mean reading score with S higher than with B? The sample mean reading score for method S was 43.0691 with a standard deviation of 5.5641 and the sample mean reading score for deviation of 5 2247. These are sample standard deviations. No alpha is provided for this problem State the null and the alternate hypotheses Ho: versus Ha: Assume that the data are independent samples from normal populations with equal population variances. Thus, we perform a pooled variance t test. Find an estimate of the pooled variance (4 decimal places) Find SP(3 decimals) Degrees of Freedom = The critical value(s) from the t table at the appropriate degrees of freedom are given by The t test statistic is Estimate the p-value State and interpret your decision:

Explanation / Answer

The test is comparison of two sample means.

n1 = 22 and n2 = 22

As sample size <30, t test can be used

H0: Mean 1 = Mean 2

Ha: Mean 1 not equals Mean 2

mean1 eq: 43.069 (variance= 30.959) (se= 1.1863)
mean2 eq: 40.077 (variance= 27.297) (se= 1.1139)

Probability that var1<var2
p=0.38786 (left: 0.6121; double: 0.7758)

Difference between means:
M1-M2=43.069-40.077=2.9923
sd=10.546; se=1.6273
95% CI of difference:
-0.1971 <2.9923< 6.1817 (Wald)
t-difference: 1.839
df-t: 41.5; p= 0.96349
(left p: 0.0365; two sided: 0.073)
Equal sd assumed
Difference not significant at 5%

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