Can someone please help me with this! I have to show my work and can use either
ID: 3218719 • Letter: C
Question
Can someone please help me with this! I have to show my work and can use either a calculator or StatDisk the program. Thanks!
When analyzing the last digits of telephone numbers in Sandtown, it was found that among 1500 randomly selected phone numbers, 225 had zero as the last digit. If the digits are selected randomly, the proportion of zeroes should be 0.1 because from probability, 0 is one of the 10 possible digits.
Use the p-value method with a 0.01 level of significance to test the claim that the proportion of zeroes is not equal to 0.1.
Use the sample data to construct a 99% confidence interval to estimate the proportion of zeroes. What does the confidence interval suggest about the claim that the proportion of zeroes is 0.1?
Compare the results from the hypothesis test and confidence interval. Do they lead to the same conclusion? Why or why not?
Explanation / Answer
to perform the statistical test , we first need to calculate the z stat as
The test statistic is a z-score (z) defined by the following equation.
z = (p - P) / , where p is sample proportion and P is population proportion
so p = 225/1500 = 0.15 and P = 0.1 and N = 1500 (given)
Compute the standard deviation () of the sampling distribution.
= sqrt[ P * ( 1 - P ) / n ]
so sqrt(0.1*0.9/1500) = 0.0077
now putting this in the first equation we get
Z = (0.15-0.1)/0.0077 = 6.49
now we check the p value in the z table as
P ( Z<6.49 )=1
hence as we see that the p value is greater than 0.01, hence we fail to reject the null hypothesis and conclude that the proportion of zeros is not equal to 0.1
no sample data is provided in the question to answer the 99% CI part of the question