Statistics & Applications PYQ

If $C$ is the original value of the asset, $S$ is the scrap value, n is the useful life of the asset and $D$ is the annual depreciation, then

A machine has been producing steel tubes of mean inner diameter of 2 cm. A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm. Test the hypothesis that the machine is working in the proper order at 5 % level of significance and answer, which of the following statements are correct? [Given that : t₉(0.05) = 2.262] (A) The value of the test statistic is t = 0.476. (B) The null hypothesis is rejected at 5 % level of significance. (C) The null hypothesis is accepted at 5 % level of significance. (D) The degree of freedom is 10. Choose the correct answer from the options given below:

A person wishes to purchase a house for ₹ 39,65,000 with a down payment of ₹ 5,00,000 and balance in equal monthly installments (EMI) for 25 years. If bank charges 6% per annum (compounded monthly), then EMI on reducing balance payment method is: [Given $(1.005)^{300} = 4.465$]

Which of the following are correct about the Sinking Fund? (A) It is a fixed term account. (B) It is a set-up for a particular upcoming expense. (C) A fixed amount at regular intervals is deposited in the Sinking Fund. (D) It can be used in any emergency. Choose the correct answer from the options given below:

For the given 5 values, 15, 18, 21, 27,39; the three year moving averages are:

An annuity in which the periodic payment begin on a fixed date and continue forever is called

If a 95% confidence interval for a population mean was reported to be 132 to 160 and sample standard deviation $\sigma = 50$, then the size of the sample in the study is: (Given $z_{0.025} = 1.96$)

The original value of an asset minus the accumulated depreciation at a given date is known as

Which of the following are the components of a time series? (A) Cyclic component (B) Regular component (C) Seasonal component (D) Economic component Choose the **correct** answer from the options given below:

Which of the following are NOT correct about "Sinking Fund"? (A) It does not have any specific purpose. (B) It can be used in any emergency. (C) Any amount, any time can be deposited in it. (D) It is set up for a particular upcoming expense. Choose the **correct** answer from the options given below:

A specific characteristic of a sample is known as a

The simple random sample consists of six observations: 5, 8, 10, 7, 10, 14. The point estimate of the population mean is:

If an investment of Rs. 12000 becomes Rs. 72000 in 4 years, then the compound annual growth rate is:

A machine costing Rs. 25000 has a useful life of 4 years. The estimated scrap value is Rs. 5000. The annual depreciation by linear method is

The present value of a sequence of payments of Rs. 2000 made at the end of every 6 months and continuing forever, if money is worth 8% per annum compounded semi-annually, is:

If 95% confidence interval for the population mean was reported to be 140 to 150 and $\sigma = 25$, then size of the sample used in this study is: [Given: $Z_{0.025} = 1.96$]

The following data shows the percentage of urban Indian households who have a high speed 5G internet connection: | Year (x) | 2020 | 2021 | 2022 | 2023 | 2024 | |---|---|---|---|---|---| | Urban house hold (y) | 9% | 18% | 21% | 29% | 38% | If a straight line trend by the method of least square for the above data is $y = 23 + 6.9(x - 2022)$, then the forecast for the year 2025 is:

Which of the following are types of "statistical inferences"? (A) Point estimation (B) Interval estimation (C) Marginal estimation (D) Hypothesis testing Choose the correct answer from the options given below:

Which of the following are examples of irregular trends in a time series? (A) Decrease in production due to a sudden strike. (B) The rise in prices before festivals (C) Unusual rise in income of the printing press due to the announcement of an election. (D) Fall in crop yield due to floods. Choose the correct answer from the options given below:

Mr. Mittal invested Rs. 20,000 in a mutual fund in the year 2019. The value of the mutual fund increased to Rs. 32,000 in the year 2024. The compound annual growth rate of his investment is: [Given $(1.6)^{1/5} = 1.098$]

Mr. X wishes to purchase a house for ₹ 14,51,400 from a bank and decided to repay the loan by equal monthly installments (EMI) in 10 years. If bank charges interest at 9 % per annum compounded monthly, then the EMI is: [Given that $(1.0075)^{120} = 2.4514]$

Which of the following is NOT correct about "Sinking Fund"?