Statistics Questions

Consider the following statements regarding index numbers:(i) Simple average of price relative is a weighted index numbering method.(ii) The index number for the base year is always 100.(iii) If the price index is 25, then the prices have increased by 25%.(iv) If the price index is 75, then the prices have decreased by 25%.Which of the statements are correct?

Calculate the index number using the simple average of price relative method for the data below, taking 2010 as the base year:ItemPrice in 2010Price in 2015A100140B80120C160200D220385E112112

A medicine is known to be $75\%$ effective. If the medicine is given to 5 patients, what is the probability that at least one patient is cured?

Given that $x\sim B(n=10,p)$, if the expectation $E(x)=8$, find the value of $p$.

A time-series data is represented by the line $y=a+bx$. If the middle time period is taken as origin ($\sum x=0$), and it is found that $\sum xy=6$ and $\sum x^2=5$, what is the value of '$b$ '?

In the same plan, how much money is allocated to both Agriculture (Angle: $90^{\circ }$) and Employment (Angle: $120^{\circ }$)?

How much excess money is allocated to Miscellaneous (Angle: $75^{\circ }$) over Education (Angle: $30^{\circ }$)?

A study investigates if the average sunlight in February was greater than the annual average of $5$ units/m${}^2$. What is the null hypothesis ($H_0$) for this problem?

In a five-year plan with a total allocation of $₹36,000$ crore, the angle for Employment is $120^{\circ }$. Which head is allocated maximum funds if the angles are Agriculture ($90^{\circ }$), Industry ($45^{\circ }$), Education ($30^{\circ }$), and Miscellaneous ($75^{\circ }$)?

In the same five-year plan (Total $₹36,000$ crore), how much money is allocated to Education if its angle is $30^{\circ }$?