A research study attempted to determine if young infants are more likely to imit
ID: 3290910 • Letter: A
Question
A research study attempted to determine if young infants are more likely to imitate actions that are modeled by a person or simulated by an object. One action examined was mouth opening. This action was modeled repeatedly by either a person or a doll, and the number of times that the infant imitated the behavior was recorded. Twenty-seven infants participated, with 12 exposed to a human model and 15 exposed to the doll. The results are shown in the chart below.
Consider the random variables of batting average and percentage of strikeouts for professional baseball players. A random sample of six professional baseball players gave the following information.
Does this sample provide significant evidence that a greater percentage of strikeouts is associated with a lower batting average? The P-value for this test is ...
a. 3.9311
b. 0.0085
c. 0.0171
d. 0.9915
48. An engineer believes he has designed an improved light bulb. The previous design had an average lifetime of 1200 hours. Using a sample of 2000 of these new bulbs, the average lifetime of this improved light bulb is found to be 1201 hours. Although the difference is quite small, the effect was statistically significant at the 0.05 level. Suppose that, in fact, there is no difference between the mean lifetimes of the previous design and the new design. Which of the following statements is true? a. A Type I error was made b. A Type II error was made c. Both Type I and Type II errors were made d. No error was madeExplanation / Answer
Solution:-
50) a. There is strong evidence (p=.004) that the mean number of imitations is significantly higher for infants who watch a human model than for infants who watch a doll.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Human< Doll
Alternative hypothesis: Human > Doll
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.571
DF = 25
t = [ (x1 - x2) - d ] / SE
t = 2.94
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 2.94. We use the t Distribution Calculator to find P(t > 2.94) = 0.0016
Therefore, the P-value in this analysis is 0.0016.
Interpret results. Since the P-value 0.0016 is less than the significance level (0.01), we have to reject the null hypothesis.
a. There is strong evidence (p=.004) that the mean number of imitations is significantly higher for infants who watch a human model than for infants who watch a doll.
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