You would like to determine if more than 50% of the observations in a population
ID: 3362725 • Letter: Y
Question
You would like to determine if more than 50% of the observations in a population are below 10. At = 0.01, conduct the test on the basis of the following 20 sample observations: Use Table 1. 12 6 5 8 5 5 7 10 13 8 11 8 12 12 8 10 9 9 9 12 Picture Click here for the Excel Data File a. Select the null and the alternative hypotheses. H0: p = 0.50; HA: p 0.50 H0: p 0.50; HA: p > 0.50 H0: p 0.50; HA: p < 0.50 b. Calculate the sample proportion. (Round your answer to 2 decimal places.) Sample proportion c. Calculate the value of test statistic. (Round your answer to 2 decimal places.) Test statistic d. The p-value is: (Round p-value to 4 decimal places.) 0.01 Picture p-value < 0.025 0.025 Picture p-value < 0.05 0.05 Picture p-value < 0.10 p-value Picture 0.10 p-value < 0.01 e. What is the conclusion? Reject H0 since the p-value is smaller than . Reject H0 since the p-value is greater than . Do not reject H0 since the p-value is smaller than . Do not reject H0 since the p-value is greater than .
Explanation / Answer
The statistical software output for this problem is:
One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5
Hypothesis test results:
Hence,
H0: p 0.50; HA: p > 0.50
Sample proportion = 0.60
Test statistic = 0.89
p - value = 0.1855
p - value > 0.10
Do not reject H0 since the p-value is greater than .
Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 12 20 0.6 0.1118034 0.89442719 0.1855Related Questions
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