Question

A local arts council has 200 members. The council president wanted to estimate the percent of its members who have had experience in writing grants. The president randomly selected 30 members and surveyed the selected members on their grant-writing experience. Of the 30 selected members, 12 indicated that they did have the experience. Have the conditions for inference with a one-sample zz-interval been met?

• Yes, all conditions for inference have been met.

  A

• No, because the sample size is not large enough to satisfy the conditions for normality.

  B

• No, because the sample was not selected at random.

  C

• No, because the sample size is not less than 10 percent of the population size.

  D

• No, because the sample is not representative of the population.

• E

Which of the following correctly compares the t-distribution and z-distribution?

• For small sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric.

  A

• For large sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric.

  B

• The curves of both distributions are symmetric, but the height of the density curve of the t-distribution is taller than the height of the density curve of the z-distribution.

  C

• The area under the density curve of the t-distribution is greater than the area under the density curve of the z-distribution, especially for small sample sizes.

  D

• The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.

• E

Answer 1

Ans 1 )we have given n = number of selected members = 30

x = number of members have experience = 12

p= proportion of members have experience = 12/30= 0.4

samples are selected randomly and n p= 30*0.4 = 12 >10

np(1-p) = 309*0.4*0.6 =7.2>5

option a is true , Yes, all conditions for inference have been met.

Ans 2 ) option E is true

The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.