Statistics & Applications PYQ — Page 10

The first m-year moving average of the data 10, 20, 30, 40, 50 is 30. The value of m is

Which of the following statements are correct? (A) The method of least squares determines the position of the trend line of the given time series. (B) The trend line is called the line of best fit. (C) The line of best fit is a line in which the sum of deviations of the actual values of the variable from their corresponding trend value is always positive. (D) The normal equations of the trend line $y = a + bx$ are $\sum y = na + b \sum x$ and $\sum xy = a \sum x + b \sum x^2$, where $n$ is the numbers of observations. Choose the *correct* answer from the options given below:

In which of the following, the time series may show the gradual shifts to relatively higher or lower values over a long period of time?

If the money is worth 8% per annum compounded semi-annually, then the present value of a sequence of payments of ₹1,000 made at the end of every 6 months and continuing forever, is:

Which of the following statements are TRUE? (A) The variable t of t-distribution ranges from $-\infty$ to $\infty$. (B) The probability curve of the t-distribution is symmetric about the line $t=0$ (C) The variance of the t-distribution is greater than one. (D) As the number of degrees of freedom decreases, the t-distribution curve moves closer to the standard normal probability curve. Choose the correct answer from the options given below:

If $(t_1, y_1)$, $(t_2, y_2)$,......,$(t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variables $y$, then

Choose the correct statement about Sinking Fund?

The following data are from a random sample: 5,8,10,7,10,14, then the point estimate of the population standard deviation is

If $r_{eff}$ = effective rate of interest, $r$ = nominal rate of interest and $m$ = number of conversion periods per year, the relationship between nominal rate and effective rate of interest is:

The term of the perpetuity 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: $(1.8)^{1/8} = 1.076$)

If CAGR stands for Compound Annual Growth Rate, F.V stands for final value of an investment, P.V stands for present value of an investment and n is the number of years then

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:

Which of the following is not correct about the Central Limit Theorem?

In reference to the Inferential Statistics, which of the following is NOT correct?

Match List-I with List-II | List-I | List-II | |---|---| | (A) A fire in a factory causing production delay for some time is | (I) Secular trend | | (B) Technological progress is | (II) Seasonal trend | | (C) The rise in prices before big festival is example of | (III) Irregular trend | | (D) Rise and fall of share market is | (IV) Cyclic trend | Choose the correct answer from the options given below:

If the following data is obtained from a simple random sample: 6, 7, 9, 10, 11, 17 Then the point estimate of population standard deviation is:

The five month moving averages for the following data | Month ($r^{th}$) | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | |---|---|---|---|---|---|---|---|---|---| | Actual Demand | 105 | 106 | 110 | 110 | 114 | 121 | 130 | 128 | 137 | is:

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:

Let two independent random samples of sizes $n_1$ and $n_2$ respectively have been drawn from the same normal population. Let $\overline{X_1}$ and $\overline{X_2}$ be the means and let $s_1$ and $s_2$ be their standard deviations. In order to test whether the the two sample means $\overline{X_1}$ and $\overline{X_2}$ differ significantly or not, the $t$-test statistic is given by

The amount to which ₹ 5000 will accumulate at the effective rate of 4% for 4 years and 5% for 2 years is

For the given five values $16, 25, 19, 34, 46$, the three years moving averages are

Which of the following are similarities between the sinking fund and the savings account? (A) The sinking fund and the savings account are both financial tools. (B) Both can be used in any emergency. (C) They both involve setting aside an amount of money for the future. (D) Both are long-term accounts which can be closed any time. Choose the correct answer from the options given below:

Which of the following are correct? (A) Time series analysis does not help to understand the behavior of a variable in the past. (B) Time series predict the future behavior of variable. (C) Time series helps to plan future operations. (D) The main aim of the time series analysis is to derive conclusions after arranging the time series in a systematic manner. Choose the correct answer from the options given below: