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Use the given confidence interval to find the margin of error and the sample mean. The sample mean is \( \square \). (Type an integer or a decimal.) The margin of error is \( \square \). (Type an integer or a decimal.)

A researcher wishes to estimate, with 95\% confidence, the population proportion of likely U.S. voters who think Congress is doing a good or excellent job. Her estima must be accurate within \( 3 \% \) of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that \( 42 \% \) of the respondents said they think Congress is doing a good or excellent job. (c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? \( \mathrm{n}=\square \) (Round up to the nearest whole number as needed.) (b) What is the minimum sample size needed using a prior study that found that \( 42 \% \) of the respondents said they think Congress is doing a good or excellent job? \( n=\square \) (Round up to the nearest whole number as needed.) (c) How do the results from (a) and (b) compare? A. Having an estimate of the population proportion reduces the minimum sample size needed. B. Having an estimate of the population proportion has no effect on the minimum sample size needed. C. Having an estimate of the population proportion raises the minimum sample size needed.

16 Use technology to construct the confidence intervals for the population variance \( \sigma^{2} \) and the population standard deviation \( \sigma \). Assume the sample is taken from a normally distributed population. \[ =0.99, s=34, n=20 \] The confidence interval for the population variance is ( \( \square \). (Round to two decimal places as needed.) The confidence interval for the population standard deviation is ( (Round to two decimal places as needed.)

THREE (3) dispersion measurements

6 The positive square root of the average of squares of deviations of the values from mean is called the \( \begin{array}{ll}\text { (a) range. } & \text { (b) arithmetic mean. } \\ \text { (c) standard deviation. } & \text { (d) mode. }\end{array} \)

5. Choose ONE (1) most appropriate quantitative variable in the study to present the students' night sleep patterns. Justify your answer. (2 marks)

Partie B : VPP et maladie rare On dispose d'un test pour dépister une maladie rare. Le fabricant du test fournit les caractéris- tiques suivantes: - la probabilité qu'un individu malade ait un test positif est de 0,99 ; - la probabilité qu'un individu non malade ait un test négatif est de 0,99 . On envisage un dépistage systématique sur une population dans laquelle on estime à \( f \) (avec \( 0 \leqslant f \leqslant 1 \) ) la proportion de gens malades. 1. Expliquer pourquoi VPP \( =\frac{99 f}{98 f+1} \).

3. ( \( \$ \) points) Major League Baseball requires that its baseballs weigh at least 142 grams and no more than 149 grams. The weights of baseballs manufactured by a particular company are normally distributed with mean 146.5 grams and standard deviation 1.9 grams. What proportion of baseballs made by this company meet the major league standard for weight? (Round your answer to 3 decimal places.)

3. (s points) Major League Baseball requires that its baseballs weigh at least 142 grams and no more than 149 grams. The weights of baseballs manufactured by a particular company are normally distributed with mean 146.5 grams and standard deviation 1.9 grams. What proportion of baseballs made by this company meet the major league standard for weight? (Round your answer to 3 decimal places.)

2. (8 points) Suppose that the weight of a particular brand of cercal in boxes labeled " 18 oz " is normally distributed with mean 18.4 oz and standard deviation 0.26 oz . What is the probability that a randomly selected box will have at least 18 oz of cereal? (Round to 3 decimal places.)