Question

In a​ survey, 45​% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result to be too​ high, so she randomly selected 210 pet owners and discovered that 93 of them spoke to their pet on the telephone. Does the veterinarian have a right to be​ skeptical? Use the alpha equals=0.01 level of significance.

-Because np 0 (1-p 0) = ___ (Choose greater, less, equal) 10, the sample size is (Choose less than, greater than) 5% of the population size, and the sample (Choose can or cannot be reasonably assumed to be random, is given to be or not to be random) the requirements for testing the hypothesis (Choose are, are not) satisfied.

-What are the null and alternative​ hypotheses?

H0: ____versus H1: ____

-Find the test​ statistic, z0

z0: ___

-Find the​ P-value

P-value:___

-Does the veterinarian have a right to be​ skeptical?

A.The veterinarian has a right to be skeptical. There is sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is not 45​%.

B.The veterinarian does not have a right to be skeptical. There is not sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is 45​%.

C.The veterinarian has a right to be skeptical. There is sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is less than 45​%.

D.The veterinarian does not have a right to be skeptical. There is not sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is less than 45​%.

Answer 1

Here we have given that,

n=number of pet owners=210 pet

x: number of pet owners spoke to their pet on the telephone=93

Now, we estimate the proportion p as

=sample proportion =

P=population proportion = 45% = 0.45

Here, Because n*P(1- P) =210*0.45*(1-0.45) =52 greater than 10, the sample size is Choose less than 5% of the population size, and the sample Choose can be reasonably assumed to be random, is given to be the requirements for testing the hypothesis Choose are satisfied.

Claim: To check whether the true proportion of pet owners who talk to their pets on telephone is less than 45 % i.e. veterinarian have right to be skeptical.

The null and alternative Hypothesis is as follows,

Ho: P = 0.45

v/s

Ho: P < 0.45

This is left one tailed test as our interest is to show P < 0.45

Now, Test statistic:

Z-statistics=

=

= -0.29

we get the test statistics = -0.29

Now we find the P-value

= level of significance= 0.05

P-value= P(Z < z) as this is left (one) tailed test  

=P(Z< -0.29)

= 0.3852

Decision:

Here, P-value( 0.3852) > 0.05

That is here we fail to reject Ho (Null Hypothesis)

Conclusion:

The veterinarian does not have a right to be skeptical. There is not sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is less than 45​%.

Here option D is correct.