o -9 points BBUnderStatt1 8 R 012 My Notes Ask Your Te. A study is made of resid

Question

o -9 points BBUnderStatt1 8 R 012 My Notes Ask Your Te. A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of 89 urban residents showed that 9 subscribed, and a random sample of 95 suburban residents showed that 15 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 5% level of significance. What are we testing in this problem? O difference of proportions O single proportion O single mean O difference of means paired difference (a) What is the level of significance? State the null and alternate hypotheses. (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. The number of trials is sufficiently large. O The Student's t. We assume the population distributions are approximately normal. The Student's t. The number of trials is sufficiently large. O The standard normal. We assume the population distributions are approximately normal. -P2. Do not use rounded values. Round your What is the value of the sample test statistic? (Test the difference P final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.

Explanation / Answer

Given that,

    N1 = 89

X1 = 9

N2 = 95

X2 = 15

Here we have to test difference of proportions.

Level of significance (alpha) = 5% = 0.05

The hypothesis for the test is,

H0 : p1 = p2   Vs       H1 : p1 > p2

Where p1 and p2 are two population proportions.

Here we use sampling distribution as the standard normal. By assuming the number of trials is sufficiently large.

We can do two proportion z-test in ti-83 calculator.

Steps :

STAT à TESTS à 6:2-PropZTest à ENTER à Input all the values à Select alternative “ > p2” à ENTER à Calculate à ENTER

Test statistic = -1.14

P-value = 0.8734

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion :

At the alpha = 0.05 level, we fail to reject the null hypothesis and conclude that the data are not statistically significant.

There is insufficient evidence at the 0.05 level to conclude that the proportion of suburban residents subscribing to sporting news is higher.

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