Suppose the teacher of secondary school B wants to conduct a similar study on DS

Question

Suppose the teacher of secondary school B wants to conduct a similar study on DSE score and collected a sample at his school as follows: The teacher believes the variance of DSE score in secondary school B is less than 25. Test his claim at a = 10%. Using the information given in Ql(c), test whether the average DSE score of the two secondary schools are different at 10% level of significance. The teacher gives an enhancement course for the sampled 10 students in secondary school B before their 2nd attempt in DSE. The 2nd attempt scores of the 10 students are recorded correspondingly. Can the teacher infer that the enhancement course is helpful at 5% significance level? 2nd attempt: 22 18 19 12 19 29 10 32 21 18 Using the information given in Ql(c) and 2nd attempt scores for secondary school B in Q2(c), the teacher now also sampled 22 students in secondary school C and found their mean and standard deviation are 23 and 5.25, respectively. Is there enough evidence to conclude that differences exist between the three secondary schools at 1% level of significance?

Explanation / Answer

a) Here we have to test the hypothesis that,

H0 : 2 = 25 Vs H1 : 2 < 25

Assume alpha = 10% = 0.1

The test statistic for testing the claim is,

X2 = (n-1)s2 / 2

where s2 is sample variance.

s2 = 1 / n-1 *(x - mean)2

n is the number of observations = 10

mean = sum of observations / number of observations = 156 / 10 = 15.6

s2 = 1 / 9*252.4 = 28.04

X2 = (10-1)*28.04 / 25 =10.096

P-value we can find by using EXCEL.

syntax is :

=CHIDIST(x,deg_freedom)

x is test statistic value.

deg_freedom = n-1 = 10-1 = 9

P-value = 3.1069E-49 = 0.000

P-value < alpha

Reject H0 at 10% level of significance.

COnclusion : Variance of DSE score in secondary school B is less than 25.

b) Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1   mu2

where mu1 and mu2 are two population means.

Here we use equal variances.

This we can done using EXCEL.

steps :

Data --> Data Analysis --> t-test: Two-Sample Assuming Equal VAriances --> ok --> Variable1Range : select first data range --> Variable2Range : select second data range --> Hypothesized mean difference : 0 --> ALpha : 0.1 --> Output Range : select one empty cell --> ok

The test statistic is,

t = -1.6293

P-value = 0.12

P-value > alpha

Accept H0 at 10% level of significance.

Conclusion : Average DSE score of the two secondary schools are same.

t-Test: Two-Sample Assuming Equal Variances Variable 1 Variable 2 Mean 15.6 20 Variance 28.04444 44.88888889 Observations 10 10 Pooled Variance 36.46667 Hypothesized Mean Difference 0 df 18 t Stat -1.62926 P(T<=t) one-tail 0.060317 t Critical one-tail 1.330391 P(T<=t) two-tail 0.120634 t Critical two-tail 1.734064

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