2. (a) Assume now that it is appropriate to use a t-distribution for a hypothesi
ID: 3236484 • Letter: 2
Question
2. (a) Assume now that it is appropriate to use a t-distribution for a hypothesis test and confidence interval for the mean u i. Test the hypothesis that the true mean IQ level (Au) of first year SPU students in 2017 is still 115. You must summarize all steps: The null (Ho) and alternative hypotheses (Ha) relevant to the research objectives stated in this scenario, the value of a suitable test statistic, specification of the appropriate t-distribution to be used as a sampling distribution for this statistic, a P-value, your summary of significance and conclusion in plain anguage ii. Produce a 95% confidence interval for the true mean IQ level of 2017 first year students at SPU Does this confidence interval include the historical mean IQ value 115? Explain whether your confidence interval is consistent with your conclu- sions from the hypothesis test in part 2(a)i (b) By referring to the boxplot obtained in part 1 briefly discuss the appropriate- ness of the use of the t-distribution as a sampling distribution for the analysis of parts 2(a)i and 2(a)iiExplanation / Answer
Answer to question# 2)
part a)
we got 36 data values
n = 36
The mean of this sample is : x bar = 130.94
The standard deviation of this sample is : s = 13.74
.
To test the claim: true mean is M = 115
.
Hypothesis:
.
Test Statistic t = (x bar - M ) / (s / sqrt(n))
Test Statistic t = (130.94 - 115) / (13.74/sqrt(36))
Test Statistic t = 6.96
.
df = 35
.
P value : For T = 6.96 , df = 35 , two tailed test is: 0.000
.
Conclusion: Since P value 0.000 < significance level 0.05 , we reject the null that the true mean is 115
Thus we conclude that the True Mean is different from 115
.
Answer to part b)
The Formula of T confidence interval is :
xbar - t * s/ sqrt(n) , xbar + t* s /sqrt(n)
T critical for df = 35 is 2.0301
.
On plugging the values we get:
130.94 - 2.0301 * 13.74 /sqrt(36) , 130.94 + 2.0301 * 13.74 /sqrt(36)
130.94 - 4.6989 , 130.94 + 4.6989
126.2411 , 135.5889
This interval does not contain 115
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