5:13 PM 42 A. 34 C. 36 B. 35 D. 37 \( \qquad \) 8. When alpha is 0.01 , confidence level is equal to \( \qquad \) A. \( 10 \% \) C. \( 90 \% \) B. \( 95 \% \) D. \( 99 \% \) 1 \( \qquad \) 9. Which of the following coefficients are the \( 95 \% \) confidence coefficients? A. \( \pm 1.65 \) C. \( \pm 2.40 \) B. \( \pm 1.96 \) D. \( \pm 2.58 \) \( \qquad \) 10. Which of the following values illustrates confidence coefficients? A. \( 99 \% \) C. 0.05 B. 1.96 D. 35.75 II. Solve each problem. Show you complete solution. 1. A confidence interval estimate has a maximum error of 2.50. If the distribution of the data where the estimate is obtained is normal with a standard deviation of 9 . a. How many samples are considered in \( 98 \% \) confidence interval estimate for the mean? b. What must be done to the sample size to reduce the margin of error of the confident interval estimate? Support your answer. 2. A researcher found that the IQ scores of the ALS students in the Division of Quezon Province are normally distributed with a mean of 110 and a standard deviation of 10 . a. How many ALS students are needed to test so that the estimate will not be more than 5 from the population mean with a \( 99 \% \) level of confidence? b. Due to limited contact with ALS students, the researcher tested a small number of ALS students. Explain the effect of this small sample on the estimate of the parameter? 2 Edit Annotate Fill \& Sign Convert
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A confidence interval estimate has a maximum error of 2.50. If the distribution of the data where the estimate is obtained is normal with a standard deviation of 9. a. How many samples are considered in 98% confidence interval estimate for the mean? The formula Show more…
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Please provide the following information for Problems $11-22$. (a) What is the level of significance? State the null and alternate hypotheses. (b) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the appropriate sampling distribution value of the sample test statistic. (c) Find (or estimate) the $P$ -value. Sketch the sampling distribution and show the area corresponding to the $P$ -value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha ?$ (e) Interpret your conclusion in the context of the application. Note: For degrees of freedom $d . f .$ not given in the Student's $t$ table, use the closest $d . f .$ that is smaller. In some situations, this choice of $d . f .$ may increase the $P$ -value by a small amount and therefore produce a slightly more "conservative" answer. Medical: Hemoglobin Count Let $x$ be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then $x$ has a distribution that is approximately normal, with population mean of about 14 for healthy adult women (see reference in Problem 17). Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are $\begin{array}{llllllllll}15 & 18 & 16 & 19 & 14 & 12 & 14 & 17 & 15 & 11\end{array}$ i. Use a calculator with sample mean and sample standard deviation keys to verify that $\bar{x}=15.1$ and $s \approx 2.51$. ii. Does this information indicate that the population average HC for this patient is higher than $14 ?$ Use $\alpha=0.01$.
Hypothesis Testing
Testing the Mean $\mu$
Please provide the following information for Problems $11-22$. (a) What is the level of significance? State the null and alternate hypotheses. (b) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the appropriate sampling distribution value of the sample test statistic. (c) Find (or estimate) the $P$ -value. Sketch the sampling distribution and show the area corresponding to the $P$ -value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha ?$ (e) Interpret your conclusion in the context of the application. Note: For degrees of freedom $d . f .$ not given in the Student's $t$ table, use the closest $d . f .$ that is smaller. In some situations, this choice of $d . f .$ may increase the $P$ -value by a small amount and therefore produce a slightly more "conservative" answer. Fishing: Trout Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is $\mu=19$ inches. However, the Creel Survey (published by the Pyramid Lake Paiute Tribe Fisheries Association) reported that of a random sample of 51 fish caught, the mean length was $\bar{x}=18.5$ inches, with estimated standard deviation $s=3.2$ inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than $\mu=19$ inches? Use $\alpha=0.05$.
Please provide the following information for Problems $11-22$. (a) What is the level of significance? State the null and alternate hypotheses. (b) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the appropriate sampling distribution value of the sample test statistic. (c) Find (or estimate) the $P$ -value. Sketch the sampling distribution and show the area corresponding to the $P$ -value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha ?$ (e) Interpret your conclusion in the context of the application. Note: For degrees of freedom $d . f .$ not given in the Student's $t$ table, use the closest $d . f .$ that is smaller. In some situations, this choice of $d . f .$ may increase the $P$ -value by a small amount and therefore produce a slightly more "conservative" answer. Medical: Red Blood Cell Count Let $x$ be a random variable that represents red blood cell (RBC) count in millions of cells per cubic millimeter of whole blood. Then $x$ has a distribution that is approximately normal. For the population of healthy female adults, the mean of the $x$ distribution is about 4.8 (based on information from Diagnostic Tests with Nursing Implications, Springhouse Corporation). Suppose that a female patient has taken six laboratory blood tests over the past several months and that the $\mathrm{RBC}$ count data sent to the patient's doctor are $\begin{array}{llllll}4.9 & 4.2 & 4.5 & 4.1 & 4.4 & 4.3\end{array}$ i. Use a calculator with sample mean and sample standard deviation keys to verify that $\bar{x}=4.40$ and $s \approx 0.28$. ii. Do the given data indicate that the population mean $\mathrm{RBC}$ count for this patient is lower than $4.8$ ? Use $\alpha=0.05$.
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