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A business school wants to compare a new method of teaching reading to slow learners to the current standard method. They decide to base this comparison on the results of a reading teat given at the end of a learning period of six months. Of a random sample of 11 slow learners. 5 are taught by the new method and 6 are taught by the standard method. All 11 children are taught by qualified instructors under similar conditions for a six month period. Assume that the populations are normally distributed and the population variances are equal.
New Method Score: 81 80 79 81 76
Standard Method Score: 69 68 71 68 73 72
Test at 1% level of significance that the new method is worse than the old method, i.e., average score obtained by the new method is less than the average score obtained by the standard method. Compute the mean and standard deviation of each data set.
State the null and the alternative hypotheses.
H0:
H1:
Write down the formula of the test statistics and find its value.
Determine the rejection region and make a decision.
Make a conclusion in the context of the problem.

Sagot :

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Answer:

Kindly check explanation

Step-by-step explanation:

New Method : 81 80 79 81 76

Standard Method Score: 69 68 71 68 73 72

H0 : μn = μa

H0 : μn < μa

New Method :

Using a calculator :

Sample size, n1 = 5

Mean, x1 = 79.40

Standard deviation, s1 = 2.07

Standard Method :

Using a calculator :

Mean, x2 = 70.17

Sample size, n2 = 6

Standard deviation, s2 = 2.14

T = (x1 - x2) / √(s1²/n1 + s2²/n)

(x1 - x1) = (79.40 - 70.17) =79.40 -= 9.23

√(s1²/n1 + s2²/n2) = √(2.07²/5) + 2.14²/6) = 1.2729

T = (x1 - x2) / √(s1²/n1 + s2²/n)

T = 9.23 / 1.2729

Test statistic = 7.25

The Pvalue from Tscore at, smaller n - 1 = 5 - 1 = 4

Pvalue = 0.000961

Decision region :

If Pvalue < α ; Reject H0 ; otherwise fail to reject H0

α = 0.01

Since, Pvalue < α ; We reject H0 ; and conclude that new method is worse rhn the old.

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