Answer:
There is not enough statistical evidence in the sample taken by the veterinarian to support his skepticism
Step-by-step explanation:
To solve this problem, we run a hypothesis test about the population proportion.
Proportion in the null hypothesis [tex]\pi_0 = 0.37[/tex]
Sample size [tex]n = 150[/tex]
Sample proportion [tex]p = 54/150 = 0.36[/tex]
Significance level [tex]\alpha = 0.05[/tex]
[tex]H_0: \pi_0 = 0.36\\H_a: \pi_0<0.36[/tex]
Test statistic [tex] = \frac{(p - \pi_0)\sqrt{n}}{\sqrt{\pi_0(1-\pi_0)}}[/tex]
Left critical Z value (for 0.01) [tex]Z_{\alpha/2}= -1.64485[/tex]
Calculated statistic = [tex]= \frac{(0.36 - 0.37)\sqrt{150}}{\sqrt{0.37(0.63)}} = -0.254[/tex]
[tex]p-value = 0.6003[/tex]
Since, test statistic is greater than critical Z, the null hypothesis cannot be rejected. There is not enough statistical evidence to state that the true proportion of pet owners who talk on the phone with their pets is less than 37%. The p - value is 0.79860.
