Statistics & Applications PYQ — Page 3

The rise and fall of share market is an example of

Mr. Vishnu has an initial investment of Rs.80,000 in an investment plan. After 3 years, it has grown to Rs.1,00,000, then his rate of return is

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

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 $(1.005)^{300} = 4.465$]

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 $z_{0.025} = 1.96$)

A person has set up a sinking fund in order to have Rs. 10,00,000 after 10 years for his child education. The amount should put bi-annually into account paying 5% per annum compounded semi-annually is: [Given $(1.025)^{20} = 1.6386$]

When the two independent small samples of sizes $n_1$ and $n_2$ with means $\bar{x}_1$ and $\bar{x}_2$ respectively are drawn from populations with identical population variances, the test-statistic is computed as

An investment of ₹ 3,00,000 becomes ₹ 4,50,000 in 5 years, then the compound annual growth rate (CAGR) is equal to: [Given that: $(1.5)^{1/5} = 1.084$]

A 95% confidence interval for a population mean was reported to be 152 to 160. If standard deviation $\sigma = 15$ . Then the sample size is : ($Z_{0.025}$=1.96)

Consider a random sample of 10 students having 116 cm as mean height and standard deviation as 9.798 cm. If the suggested mean height of the students population is 110 cm then the t-test statistic of the sample is: [given $\frac{\sqrt{10}}{9.798} = 0.3227$]

A motorcycle has a scrap value of Rs. 22,500 after 15 years of its purchase. If the annual depreciation charge is Rs. 8,500, then the original cost by linear method is:

The effective rate of return equivalent to a nominal rate of 12% per annum compounded quarterly is: [Given that: $(1.03)^4 ≈ 1.1255$]

The behavior and pattern of the data in a time series is NOT based on which of the following component?

If $y = a + b(x - 2022)$ is a straight line trend using the least square method for the following data | Year ($x$) | 2020 | 2021 | 2022 | 2023 | 2024 | |---|---|---|---|---|---| | Profit (Rs. '000) ($y$) | 2 | 3 | 4 | 5 | 2 | Then the value of $\frac{a}{b}$ is:

A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150. If the population mean is 56 then the value of t-test statistic is:

Mrs Rathna invested Rs 2 lakh in an enterprise for 5 years. Her compound annual growth rate (CAGR) turned out to be 20.5%. The end balance would be: (given $(1.205)^5=2.54)$

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: $[given \, that(1.6)^{1/5} = 1.098]$

If $y = 38.85 + 7.64(x - 2020)$ is the equation of the straight line trend for the following data: | Year $(x)$ | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | |---|---|---|---|---|---|---|---| | Profit (Rs. '000) $(y)$ | 14 | 30 | 26 | 44 | 38 | 56 | 64 | The trend value for the year 2021 by least square method is:

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:

A machine costing Rs 50,000 has a useful life of 4 years.The estimated scrap value is Rs 10,000 . The rate of depreciation per annum is:

A piece of machinery is bought for Rs. 50,000. In the first year, it depreciates by 15%, and in each subsequent year, the depreciation rate increases by 5% from the previous year. The value of machinery after 3 years will be:

Increase in the number of patients in the hospitals due to heat stroke is:

| Year (t) | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | |---|---|---|---|---|---|---|---| | Sales (in Rs. crores) (y) | 6 | 8 | 9 | 11 | 13 | 17 | 20 | In reference to the above data, which of the following statements are correct? (where $x = t - 2013$) (A) If the equation of the straight line trend is $y = 12 + 2.29 x$, then the trend value for the year 2017 is 21.16. (B) If the equation of the straight line trend is $y = 12 + 2.29 x$, then the trend value for the year 2013 is 11. (C) If the equation of the straight line trend is $y = 12 + 2.29 x$, then the trend value for the year 2015 is 17. (D) If $(t_1, y_2),(t_2, y_2),(t_3, y_3),......,(t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variable y, then $\sum(y - y_t) = 0$. Choose the correct answer from the options given below:

A machine costing ₹ 1,00,000 has a useful life of 5 years. The estimated scrap value is ₹ 20,000. Using straight line method the annual depreciation is