A study of young children was designed to increase their intake of whole-grain,
ID: 3323947 • Letter: A
Question
A study of young children was designed to increase their intake of whole-grain, rather than regular-grain, snacks. At the end of the study, the 78 children who participated in the study were presented with a choice between a regular-grain snack and a whole-grain alternative. The whole-grain alternative was chosen by 54 children. You want to examine the possibility that the children are equally likely to choose each type of snack. (a) Formulate the null and alternative hypotheses for this setting Ho: p-0.5 Ho: p 0.5 Ha: p 0.5 Ho: p > 0.5 H: p s 0.5 (b) Are the guidelines for using the large-sample significance test satisfied for testing this null hypothesis? Explain your answer Yes, the conditions were met. The expected number of successes and the expected number of failures were both greater than 10 Yes, the conditions were met. The expected number of successes and the expected number of failures were both less than 10 No, the conditions were not met. The expected number of successes and the expected number of failures were both greater than 10 No, the conditions were not met. The expected number of successes and the expected number of failures were both less than 10 (c) Perform the significance test. (Use = 0.01. Round your test statistic to two decimal places and your P-value to four decimal places.) P-value = Summarize your results in a short paragraph Reject the null hypothesis. There is not significant evidence that children are not equally likely to choose each kind of snack Reject the null hypothesis. There is significant evidence that children are not equally likely to choose each kind of snack. Fail to reject the null hypothesis. There is significant evidence that children are not equally likely to choose each kind of snack. Fail to reject the null hypothesis. There is not significant evidence that children are not equally likely to choose each kind of snack.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,
a) Hypotheses: Option A is correct.
b) Option A is correct.
c) z = 3.40
P = 0.0007
Summarization: Option B is correct.
Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 54 78 0.69230769 0.056613852 3.3968311 0.0007Related Questions
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