Question

A package delivery service wants to compare the proportion of on-time deliveries for two of its major service areas. In City A, 243 out of a random sample of 300 deliveries were on time. A random sample of 297 deliveries in City B showed that 226 were on time.

1. Calculate the difference in the sample proportion for the delivery times in the two cities.

?̂ ?????−?̂ ????? =

2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of deliveries that are on time in City A is different from than the proportion in City B?

A. ?0:??=??, ??:??≠??
B. ?0:??=??, ??:??>??
C. ?0:??=??, ??:??<??

3. Calculate the pooled estimate of the sample proportion.

?̂  =

4. Calculate the test statistic for this hypothesis test.

? =

5. Calculate the p-value for this hypothesis test.

p-value =

7. Based on the p-value, we have:
A. very strong evidence
B. strong evidence
C. extremely strong evidence
D. some evidence
E. little evidence
that the null model is not a good fit for our observed data.

8. Compute a 99% confidence interval for the difference ?̂ ?????−?̂ ?????.

( , )

Answer 1

given data are:-

1).the difference in the sample proportion for the delivery times in the two cities.

= ( 0.81-0.7609)

= 0.0491

2).hypothesis:-

3). the pooled estimate of the sample proportion be:-

4).the test statistic for this hypothesis test be:-

5).the p-value for this hypothesis test be:-

= 2* P(Z>1.46)

= 2* (1-0.927855) [ in any blank cell of excel type =NORMSDIST(1.46) press enter]

= 0.1441

7. Based on the p-value, we have:-little evidence
that the null model is not a good fit for our observed data.

[ p value = 0.1441 > 0.05 (alpha)

so, we fail to reject the null hypothesis]

8).z critical value for 99% confidence interval be:-

the 99 % confidence interval for the difference be:-

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