B. (0.50 pts.) Do these results provide evidence for preferential helping at the nests of kin? Conduct the appropriate test. QUESTION 2: Each member of a large geneties class grows 12 pea plants from an independent Dea family. Each family is expected to have \( 3 / 4 \) plants with smooth peas and 1/4 plants with wrinkled peas. A. \( (0.50 \mathrm{pts} \) ) On average, how many wrinkled pes plants will a student see in her 12 plants? B. \( (0.25 \mathrm{pts} \).\( ) What is the standard deviation of the proportion of wrinkled pea plants per \) student? C. \( (0.25 \mathrm{pts} \). What is the variance of the proportion of wrinkled pea plants per student? D. \( (0.50 \) pts.) Predict what proportion of the students saw exactly two wrinkled pea plants in their sample. QUESTION 3: In North America, between 100 million and 1 billion birds dic each year by
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Paired Differences Test For a random sample of 20 data pairs, the sample mean of the differences was $2 .$ The sample standard deviation of the differences was $5 .$ Assume that the distribution of the differences is mound-shaped and symmetric. At the $1 \%$ level of significance, test the claim that the population mean of the differences is positive. (a) Check Requirements Is it appropriate to use a Student's $t$ distribution for the sample test statistic? Explain. What degrees of freedom are used? (b) State the hypotheses. (c) Compute the sample test statistic and corresponding $t$ value. (d) Estimate the $P$ -value of the sample test statistic. (e) Do we reject or fail to reject the null hypothesis? Explain. (f) Interpretation What do your results tell you?
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Forty randomly selected students were asked the number of pairs of sneakers they owned. Let $X=$ the number of pairs of sneakers owned. The results are as follows: $$\begin{array}{|l|l|} \hline X & \text { Frequency } \\ \hline 1 & 2 \\ \hline 2 & 5 \\ \hline 3 & 8 \\ \hline 4 & 12 \\ \hline 5 & 12 \\ \hline 6 & 0 \\ \hline 7 & 1 \\ \hline \end{array}$$ a. Find the sample mean, $\overline x$ b. Find the sample standard deviation, s. c. Construct a histogram of the data. d. Complete the columns of the chart. e. Find the first quartile. f. Find the median. g. Find the third quartile. h. Construct a box plot of the data. i. What percentage of the students owned at least five pairs? j. Find the $40^{\text {th }}$ percentile. k. Find the $90^{\text {th }}$ percentile. 1. Construct a line graph of the data. m. Construct a stemplot of the data.
A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 10 and the sample standard deviation is $2 .$ Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is $9.5 .$ (a) Is it appropriate to use a Student's $t$ distribution? Explain. How many degrees of freedom do we use? (b) What are the hypotheses? (c) Compute the $t$ value of the sample test statistic. (d) Estimate the $P$ -value for the test. (e) Do we reject or fail to reject $H_{0} ?$ (f) Interpret the results.
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