Question

7. The following table gives the number of aircraft accidents that occurs during the
various days of week. Find whether the accidents are uniformly distributed over the
week.
Days Sun Mon Tue Wed Thr Fri Sat
No. of accidents 14 16 8 12 11 9 4
(Given: The values of chi-square significant at 5,6,7 degrees of freedom are
respectively 11.07,12.59, 14.07 at 5% level of significance).

Answer 1

Answer:

Null hypothesis (H0): Accidents are equally distributed over all the days of week.

Alternative Hypothesis (Ha) : Accidents do hot occur equally.

ii. Calculation of test statics: If the accidents occur equally on all days of a week, than there will be 847=12 accident per day, i.e E=12

Day Observed frequency (O) Expected Frequency (E) (O−E)2 X2=(O−E)2E

Sun 13 12 1 0.0833

Mon 15 12 9 0.75

Tue 11 12 1 0.0833

Wed 9 12 9 0.75

Thu 12 12 0 0

Fri 10 12 4 0.3333

Sat 14 12 4 0.3333

Total ∑x2 = 2.33

iii. Level of significance: α = 0.05

Degree of freedom = h-1

=7-1

=6

iv Critical value ⇒ For 6 degrees of freedom at 5% level of significance table value.

x2 is 12.59

v. Decision ⇒ Since the calculated value of x2 is less than the table value. The hypothesis is accepted.

∴ The accidents occur equally on all working days.

Answer 2

Concept:

The null hypothesis is a statistical claim that no statistical significance can be found in a set of given observations. To determine the validity of a theory, hypothesis testing is carried out using sample data. Its sign is H0, and it is occasionally referred to as simply "the null."

Quantitative analysts use the null hypothesis, also referred to as the conjecture, to determine whether a theory about markets, investing techniques, or economies is valid or incorrect.

For instance, a gambler can be curious about how fair a game of chance is. The projected earnings per play for both participants equal 0 if it is fair.  The gambler gathers earnings information from numerous iterations of the game, computes the average earnings from these data, and then tests the null hypothesis that the expected earnings are identical to zero.

A null hypothesis, which is a statistical postulate, states that specific characteristics of a population or a data-generation process are not different from one another.

For example, a gambler would be interested in learning how fair a game of chance is. If it is fair, the expected earnings per play for both players equal zero. If the game is unfair, the expected earnings are positive for one player and negative for the other. In order to test the null hypothesis that the expected profits are equal to zero, the gambler collects data on winnings from several iterations of the game, computes the average winnings using these data, and then examines the data.

Given:

Days Sun Mon Tue Wed Thr Fri Sat

No. of accidents 14 16 8 12 11 9 4

Find:

If accidents are uniformly distributed or not

Solution:

Air craft accidents are uniform over the week

#SPJ2