(Round all intermediate calculations to at least 4 decimal places.) A television
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Question
(Round all intermediate calculations to at least 4 decimal places.)
A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. For this to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network will keep its current lineup of shows unless the majority of the customers want to watch the new show. The network receives 1,228 responses, of which 743 indicate that they would like to see the new show in the lineup. Use Table 1.
Select the hypotheses to test if the television network should give its newest television show a spot during prime viewing time at night.
Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Calculate the critical value at = 0.01. (Round your answer to 2 decimal places.)
(Round all intermediate calculations to at least 4 decimal places.)
A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. For this to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network will keep its current lineup of shows unless the majority of the customers want to watch the new show. The network receives 1,228 responses, of which 743 indicate that they would like to see the new show in the lineup. Use Table 1.
Explanation / Answer
(a)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: H0: p < 0.50
Alternative hypothesis: HA: p > 0.50
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too large.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ] = sqrt [(0.5 * 0.5) / 1228)] = 0.01426825363 or 0.0143
z = (p - P) / = (0.61 - 0.50)/0.0143 = 7.6923
Critical value = - 2.3263
We use the Normal Distribution Calculator to find P(z < 7.6923)
The P-Value is < 0.00001.
The result is significant at p < 0.01.
Interpret results. Since the P-value is less than the significance level (0.01), we cannot accept the null hypothesis.
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