Refer to the Early Childhood Education Journal (Mar. 2014) study of interactions in a children's museum. (Interactions by visitors to the museum included show-and-tell, learning, teaching, refocusing, participatory play, advocating, and disciplining interactions.) Recall that the researchers observed a sample of 170 meaningful interactions, of which 81 were led by children and 89 were led by adult caregivers. a. Give a point estimate of the true proportion of all meaningful interactions in a children's museum that are led by children. b. Form a 90% confidence interval around the proportion, part a. c. Interpret the interval, part b, in the words of the study. d. Suppose an educator claims that the true proportion of all meaningful interactions in a children's museum that are led by children is 35%. Make an inference about this claim.

Which of the following is the time of fastest growth in a person's life? (a) Infancy, (b) Early childhood, (c) Middle childhood, (d) Late childhood.

What is the Reggio Emilia early-childhood program?

Use the definition of the derivative to find each of the following. $\frac{d}{d x}(3-2 x)$

When asked, "How much time will you require to complete this task?", cognitive theory posits that people will typically underestimate the time required. Would the opposite theory hold if the question was phrased in terms of how much work could be completed in a given amount of time? This was the question of interest to researchers writing in Applied Cognitive Psychology (Vol. 25, 2011). For one study conducted by the researchers, each in a sample of 40 University of Oslo students was asked how many minutes it would take to read a 32-page report. In a second study, 42 students were asked how many pages of a lengthy report they could read in 48 minutes. (The students in either study did not actually read the report.) Numerical descriptive statistics (based on summary information published in the article) for both studies are provided in the accompanying table.

$$\begin{matrix} \text{ } & \text{Estimated Time (minutes)} & \text{Estimated Number of Pages}\\ \text{Sample size, n} & \text{40} & \text{42}\\ \ {Sample \ mean, \ \bar{x}} & \text{60} & \text{28}\\ \text{Sample standard deviation, s} & \text{41} & \text{14}\\ \end{matrix}$$

The researchers determined that the actual mean time it takes to read the report is $\mu=48$ minutes. Is there evidence to support the theory that the students, on average, will overestimate the time it takes to read the report? Test using $\alpha=.10$.

The mean and standard deviation of a random sample of n measurements are equal to 33.9 and 3.3, respectively. Find a 95% confidence interval for

$$\mu \text { if } n = 100$$

A 1-kg bucket resting on the ground initially contains 6 kg of water. The bucket is lifted from the ground at a constant rate, and while it is rising, water leaks out of the bucket at a constant rate of $\frac{1}{4} \mathrm{kg} / \mathrm{m}$. How much work is required to lift the bucket a vertical distance of 8 m? Assume the weight of the rope used in raise the bucket is negligible.

If p is near 0 or 1, how large a sample is needed to employ the large-sample confidence interval procedure?

Solve. f - $1.64 =$3.77

Give the z -score for a measurement from a normal distribution for the following: 1 standard deviation above the mean

A random sample of 100 observations from a population with standard deviation 60 yielded a sample mean of 110. Test the null hypothesis that

$$\mu = 100$$

against the alternative hypothesis that

$$\mu > 100 , \text { using } \alpha = .05$$

Interpret the results of the test.

For the binomial sample information summarized in each part, indicate whether the sample size is large enough to use the methods of this chapter to construct a confidence interval for p .

$$\begin{array} { l } { \text { a. } n = 500 , \hat { p } = .05 } \\ { \text { b. } n = 100 , \hat { p } = .05 } \\ { \text { c. } n = 10 , \hat { p } = .5 } \\ { \text { d. } n = 10 , \hat { p } = .3 } \end{array}$$

In a test of

$$H _ { 0 } : \mu = 100 \text { against } H _ { a } : \mu \neq 100$$

the sample data yielded the test statistic z = 2.17. Find the p -value for the test.

Decide whether the following statement is true or false:
Children’s self-esteem is extraordinarily high in early childhood.

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