Statistics & Applications PYQ — Page 8

Data available for profit (₹ Thousands) of a company as | Year | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | |---|---|---|---|---|---|---|---| | Profit(₹ 000) | 114 | 130 | 126 | 144 | 138 | 156 | 164 | Based on the above data using least square method the trend value for the year '2007' is

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:

Consider the following hypothesis test: $H_0: \mu = 18$ $H_1: \mu \neq 18$ If a sample of 48 provided a sample mean $\bar{x} = 17$ and a sample standard deviation $\sigma = 4.5$, then the value of the t-test statistic is:

Consider the following hypothesis test. $H_0: \mu \leq 12$ $H_a: \mu > 12$ If a sample of 25 is taken with sample mean 15 and a sample standard deviation of 6, then the value of t-test statistic is:

Consider the following hypothesis test: $H_0: \mu \leq 12$ $H_a: \mu > 12$ A sample of 25 provided a sample mean $\bar{x} = 14$ and a sample standard deviation $s = 4.32$. If $t_{0.05} = 1.711$, then which of the following is correct? (A) The test statistic is defined as $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$. (B) The value of the test statistic is 1.31. (C) At $\alpha = 0.05$, the null hypothesis is rejected. (D) If the value of the t-statistic is less than $t_\alpha$, then null hypothesis is accepted. Choose the correct answer from the options given below:

Consider the following hypothesis test: $H_0: \mu \leq 3432$ $H_a: \mu > 3432$ A sample of 96 provided a sample mean $\bar{x} = 3648$ and sample standard deviation $s=802$ then the degree of freedom of t-distribution is:

Consider the following hypothesis test: $H_0: \mu \leq 16$ $H_a: \mu > 16$ A sample of 25 provided a sample mean $\bar{x} = 17$ and a sample standard deviation $s = 3.5$, then the value of the test statistic in $t$-test is:

Consider the following hypothesis test, $H_0: \mu = 15$ $H_a: \mu ≠ 15$ A sample of 50 provided a sample mean of 14.15. If the sample standard deviation is 3, then the value of the test statistic t0-test is

Consider the following hypothesis test:- H₀: μ = 20 H₁: μ ≠ 20 A sample of 40 provided a sample mean of 19. The standard deviation is 3. Then the value of the t-test statistic is:

Consider the following hypothesis $H_0: \mu = 315$ and $H_a: \mu \neq 315$ A sample of 60 provided a sample mean of 324.6. The standard deviation ($\sigma$) is 14 and level of significance $\alpha = 0.05$. Then the confidence interval is: [Given: $Z_{a/2}{\frac{14}{\sqrt60}} = 3.54$]

Consider the following data | Year (x) | 2014 | 2016 | 2018 | 2020 | 2022 | 2024 | |---|---|---|---|---|---|---| | Profit (in Rs. Thousand) (y) | 7 | 9 | 10 | 12 | 14 | 14 | Then for the above data the equation of straight line trend by method of least square is given by:

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

Consider the following data: | Year (x) | 2010 | 2011 | 2012 | 2013 | 2014 | |---|---|---|---|---|---| | Sale (in crore Rs.) (y) | 9 | 18 | 21 | 29 | 38 | A straight line trend by the method of least square is:

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

Consider the following data of expenses (in lakhs) of an organization year wise | Year | 2001 | 2002 | 2003 | 2004 | 2005 | |---|---|---|---|---|---| | Expenses (Rs. lakh) | 160 | 185 | 220 | 300 | 510 | Then expected expenses trends for the year 2006 using method of least square is:

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 $\frac{\sqrt{10}}{9.798} = 0.3227$]

Components of Time Series are (A) Secular Trend Component (B) Seasonal Component (C) Moving Average Component (D) Cyclical Component Choose the **correct** answer from the options given below:

Choose the correct statement about Sinking Fund?

Choose the correct statement about CAGR(compound annual growth rate)?

Calculate Three Yearly moving averages for the following data | Year | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | |---|---|---|---|---|---|---| | Production (thousand tonnes) | 200 | 220 | 231 | 254 | 202 | 243 |

Based on the data available for the production ($y_i$ in thousand tons) of a cloth factory for 7 years ($x_i$) using the method of least squares, the straight line trend is given by $y - a + bx$ with $\sum y_i = 608, \sum x_i = 0, \sum x_iy_i = 116, \sum x_i^2 = 28$. Then, the increase in production per year is:

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

At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 40000?

At what rate of interest will the present value of a perpetuity of ₹ 600 payable at the end of every 3 months be ₹ 18,000?