Class 12 CBSE Applied Maths Inferential Statistics Exercise 10.3
Class 12 CBSE Applied Maths aims to develop an understanding of basic
mathematical and statistical tools and their
applications in the field of commerce (business/ finance/economics) and social
sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and
Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index
Numbers and Time-based data , Financial Mathematics , Linear Programming.
Please Select
Q1.
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Q2.
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Q3.
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Q4.
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Q5.
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Q6.
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Q7.
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Q8.
In India salaried individuals filling income tax returns received an average refund of Rs 1056.
Consider the population of last minute income tax payers who file their tax return during
the last five days of the income tax period.
(i) A researcher suggests that a reason individuals wait until last five days is that on
average these individuals receive lower refunds than do early fillers.
Develop appropriate hypothesis such that rejection of Hg will support the researcher’s
point of view.
(ii) For a sample of 400 individuals who filled a tax return in last five days, the sample
mean refund was Rs 910. Based on prior experience a population standard deviation of
σ = Rs 1600 may be assumed, what is the p-value?
(iii) At σ = 0.05, what is your conclusion?
(iv) Repeat the preceding hypothesis test using the critical value approach.
Solution :
Q9.
ABC Infra an Indian real estate research firm, tracks the cost of apartment rentals in Mumbai.
In mid 2016, the mean apartment rental rate was Rs 62650 per month in Mumbai. Assume
that based on quarterly surveys, a population standard duration σ = Rs 15750 is reasonable.
In a current study of apartment rental rates, a sample of 180 apartments in Mumbai has the
mean rental rate Rs 61250 per month. Do the sample date enable ABC Infra to conclude that the population mean apartment rental rate now exceeds the level reported in 2016?
(i) State null and alternative hypothesis.
(ii) What is the p-value?
(iii) Ato = 0.01, what is your conclusion?
Solution :
Q10.
She average annual total return for SBI global advantage mutual fund from 1999 to 2003 was 4.1%. A researcher would like to conduct a hypothesis test to see whether the returns for PNB growth mutual funds over the same period are significantly different from the average for SBI global advantage mutual funds,
(i) Formulate the hypothesis that can be used to determine whether the mean annual return for PNB growth funds differ from the mean for SBI global advantage funds.
(ii) A sample of 40 PNB growth funds provides a mean return of x-(x bar) = 3.4%. Assume the
population standard deviation for PNB growth funds is known from previous studies
to be σ = 2%. Use the sample results to compute the test statistic and p-value for the
hypothesis test.
(iii) At α = 0.05, what is your conclusion?
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