Statistics & Applications PYQ — Page 5

Consider the following data: | Year (X) | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | |---|---|---|---|---|---|---|---| | Profit (₹) (y) | 114 | 130 | 126 | 144 | 138 | 156 | 164 | The equation of straight line trend by using least square method is $y = 138.86 + 7.64 (x - 2007)$, then the trend values for the year 2004 is

Ajesh has set up a sinking fund in order to have ₹ 10,00,000 after 10 years for his son's education. The amount should be set aside at the end of every 6 months into an account paying 5% per annum compounded half yearly is: [given $(1.025)^{20} = 1.6386$]

A machine costing ₹ 36000 has an effective life of 5 years with scrap value of ₹ 5000 following a linear method of depreciation. Which of the following statements are **correct**? (A) The value of the machine after 1 year is ₹ 31000 (B) The value of the machine after 2 years is ₹ 23600 (C) The value of the machine after 3 years is ₹ 18400 (D) The value of the machine after 4 years is ₹ 11200 Choose the **correct** answer from the options given below:

Match List-I with List-II | List-I | List-II | |---|---| | **Example** | **Time-series component** | | (A) Labour strike | (I) Secular-trend | | (B) Continuous decline in death rate | (II) Seasonal | | (C) Rise in prices before Diwali | (III) Cyclical | | (D) Rise and fall of the share-market | (IV) Irregular | Choose the **correct** answer from the options given below:

At what rate of interest will the present value of a perpetuity of ₹ 500 payable at the end of every 6 months be ₹ 20,000?

Rajesh calculated 95% confidence level. What does he mean by that? (A) He can be 95% confident that his sample will include the population parameter. (B) He can be 95% confused that his sample will include the population parameter. (C) He can be 5% confident that his sample will not include the population parameter. (D) He can be 5% confident that his sample will include the population parameter. Choose the **correct** answer from the options given below:

Which of the following are correct about t-test statistics? (A) The mean of t-test distribution is 0. (B) It depends on the degrees of freedom. (C) It depends on population standard deviation. (D) With more degrees of freedom, it closely resembles standard normal distribution. Choose the **correct** answer from the options given below:

A 95% confidence interval for a population mean was reported to be 152 to 160. If sample standard deviation $\sigma=15$, then sample size used in this study is (Given $Z_{0.025}=1.96$)

If three year moving averages for five data items given by 16, 18, 20, 10, 21 are $x$, $y$ and $z$ respectively, then:

The declared rate of return compounded semi annually equivalent to the effective rate of return 10.25% per annum is:

The values of '$a$' and '$b$' if the equation of straight line trend by least square method is given by $y = a + bx$ such that $\sum x = 0$, $\sum y = 84$, $\sum xy = 108$, $\sum x^2 = 70$ for 6 observation at are:

Rahul invested ₹ 20000 in a mutual fund in year 2018. If the value of mutual fund increased to ₹ 32000 in year 2023. Then the compound annual growth rate of his investment is: $[given \, that(1.6)^{1/5} = 1.098]$

Anush takes a loan of ₹ 150000 @ 16% annual interest for 5 years. His EMI (Equally Monthly Installment) on monthly basis under flat rate system is:

Anisha invested Rs.20000 in a mutual fund in the year 2016, which increased to Rs.36000 in the year 2024. The percentage compounded annual growth rate(CAGR) of her investment is: (Given: $(1.8)^{1/8} = 1.076$)

Match List-I with List-II | List-I | List-II | |---|---| | Time Series Component | Example | | (A) Secular Variation | (I) Pandemic | | (B) Seasonal Variation | (II) Recession in business | | (C) Cyclic Variation | (III) Monthly sale of woolen cloths | | (D) Irregular variation | (IV) Data regarding National income | Choose the correct answer from the options given below:

Match List-I with List-II | List-I | List-II | |---|---| | Terms | definition | | (A) POPULATION | (I) Measurable characteristics of the population such as mean, variance, standard deviation etc. of population | | (B) SAMPLE | (II) Measurable characteristics of the sample such as mean, variance, standard deviation etc. of a sample | | (C) PARAMETER | (III) Finite set of statistical individuals drawn from a population for investigation. | | (D) STATISTIC | (IV) Collection of objects having the same characteristics | Choose the correct answer from the options given below:

At what rate will the present value of a perpetuity of Rs.1000 payable at the end of each quarter be Rs.50000?

Consider the following data | Year (x) | 2010 | 2011 | 2012 | 2013 | 2014 | |---|---|---|---|---|---| | Profit (Rs. in thousands) (y) | 10 | 12 | 14 | 16 | 13 | The equation of straight line trend by method of least square for the above data is given by

With reference to sampling, which of the following are correct? (A) Simple random sampling is probability sampling (B) Snow-ball sampling is non-probability sampling (C) Stratified sampling is probability sampling (D) Cluster sampling is non-probability sampling Choose the correct answer from the options given below:

The annual depreciation of an asset is independent of:-

The amount should be deposited at the end of every 6 months to accumulate Rs.50,000 in 8 years if money is worth 6% p.a. compounded semiannually, is: [Given $(1.03)^{16} = 1.6047$]

The point estimate of the population standard deviation as per the below mentioned data from a simple random sample 6,10,15,12,9,8 will be :-

Consider the following test: H₀: μ ≤ 12 H₁: μ > 12 A sample of 36 provided a sample mean $\bar{x} = 16$ and a sample standard deviation S=4.2. Then the value of the t- test statistic is:

Vatsala buys a car for Rs.7,00,000 and pays upfront Rs.2,50,000 through her credit card. The balance is to be paid in 5 years by equal monthly installments at an interest of 7% per annum as reducing balance. The EMI to be paid by Vatsala will be :- [given (1.0058)⁻⁶⁰=0.7068]