True or False. Justify for full credit. If A and B are any two events, then P(A

Question

True or False. Justify for full credit. If A and B are any two events, then P(A ANDB) = P(A)+P(B). If the variance of a data set is 0, then all the observations in this data set must be identical. A normal distribution curve is always symmetric to its mean When plotted on the same graph, a distribution with a mean of 60 and a standard deviation of 5 will look more spread out than a distribution with a mean of 40 and standard deviation of 8. In a left-tailed test, the value of the test statistic is -2. The test statistic follows a distribution with the distribution curve shown below. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.

Explanation / Answer

(A) If A and B are any two events then P(A AND B)= P(A) + P(B)

==> FALSE

(B) If the variance of data set is null then all observations in the data set must be identical

==> True. Variance represnet the variation (or spread) of data from it's mean. If Variance is 0 it means there is no variation present in the data from mean value. Hence all observations in the data are identical

(c) A Normal distribution curve is always symmetric about it's mean.

==> True

(d) False.

Standard deviation for first distribution is 5 and for second it is 8 so spread of first distribution from mean is less than spread of second distribution. Hence the second distribution plot will look like more spread than first.

(e) True

The test is left tailed test, and test statistic value is -2. Level of significance is 0.05

P-value for left tailed test is = P(z < z cal) = P(Z < -2)

Now from above graph we know the Z distribution is symmetric about its mean so area above 2 and area below -2 is same

p-value = P(Z > 2) = 0.03

We reject the null hypothesis if p-value < 0.05 which is true in given case as 0.03< 0.05.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.