Statistics & Applications PYQ — Page 11

For the given 5 values 24, 18, 33, 42, 24; the 3-year moving averages are:

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:

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 :-

Which of the following statements are correct about the "Central Limit Theorem"? (A) The sampling distribution of the sample mean approaches the normal distribution as the sample size gets larger. (B) A sample size of 30 or more is considered to be sufficient to hold the "Central Limit Theorem". (C) As the sample size becomes larger, the prediction of characteristics of the population becomes more accurate. (D) The sampling distribution of the sample mean approaches a bell shaped curve as the sample size gets larger. Choose the correct answer from the options given below:

At 6% converted quarterly, the present value of a perpetuity of ₹ 900 payable at the end of each quarter is:

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

Every year the price of a motorcycle depreciates by Rs. 15000. After 12 years its price has become Rs. 50000. Then its original cost was:

A Multinational company creates a sinking fund by setting a sum of ₹ $12,000$ annually for $10$ years to pay off a bond issue of ₹ $72,000$. If the fund accumulates at $5 \%$ per annum compound interest, then the surplus after paying for bond is : (Use $\left.(1.05)^{10} \approx 1.6\right)$

If $95 \%$ confidence interval for the population mean was reported to be $160$ to $170$ and $\sigma=25$, then size of the sample used in this study is: (Given $\mathrm{Z}_{0.025}=1.96$ )

Ms. Sheela creates a fund of ₹ $1,00,000$ for providing scholarships to needy children. The scholarship is provided in the beginning of the year. This fund earns an interest of $r \%$ per annum. If the scholarship amount is taken as ₹ $8,000$, then $r=$

Match List-I with List-II: | List-I Property Type | List-II EMI amount (in ₹) | | --- | --- | | (A) P | (I) 25,600 | | (B) Q | (II) 38,400 | | (C) R | (III) 32,000 | | (D) S | (IV) 35,200 |

The following data is from a simple random sample : $15,23, x, 37,19,32$ If the point estimate of the population mean is $23$, then the value of $x$ is :

For an investment, if the nominal rate of interest is $10 \%$ compounded half yearly, then the effective rate of interest is :

Which of the following are components of a time series ? (A) Irregular component (B) Cyclical component (C) Chronological Component (D) Trend Component Choose the **correct** answer from the options given below :