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It is known that 75% of all brand A external hard drives work in a satisfactory manner throughout the warranty period (are "successes"). Suppose that n = 15 drives are randomly selected. Let X = the number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. What is the sampling distribution of this statistic:
X/n and p(X/n) when X=1?
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- Consider a binomial process with proportion p = 1/5. Now consider the calculation of the sample proportion p = 2 where x is the number of successes and n = 40 is the number of trials. n (a) What is the mean of the sampling distribution for p? (b) What is the standard deviation of the sampling distribution for p? (c) Now consider doubling the number of trials to n = = 80. How does this affect the mean and standard deviation of the sampling distribution for p? Do they change? If so, what are the new values? Does this lead to a better or worse estimation of the true proportion p?The average wait time to get seated at a popular restaurant in the city on a Friday night is 7 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 12 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 9, 5, 5, 7, 8, 5, 7, 7, 9, 5, 6, 9 What can be concluded at the the a = 0.10 level of significance level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: pv = 7 H: pv> c. The test statistic t v = -0.352 (please show your answer to 3 decimal places.) d. The p-value = 0.3657 X (Please show your answer to 4 decimal places.) e. The p-value is >vV a vX the null hypothesis. f. Based on this, we should reject g. Thus, the final conclusion is that ... O The data suggest the populaton mean is significantly more than 7 at a = 0.10, so there is statistically significant evidence to conclude that the population mean wait time…The average wait time to get seated at a popular restaurant in the city on a Friday night is 7 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 12 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 9, 5, 5, 7, 8, 5, 7, 7, 9, 5, 6, 9 What can be concluded at the the a = 0.10 level of significance level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: P Select an answer H1: pv Select an answer v c. The test statistic (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is >v f. Based on this, we should Select an answer the null hypothesis. g. Thus, the final conclusion is that .. O The data suggest the populaton mean is significantly more than 7 at a = 0.10, so there is statistically significant evidence to conclude that the population…
- The result of anationwide aptitude test in Mathematics are normally distributed with μ=84 and sd=16. What is the raw score such that 78% of the cases are below it?The 11 participants in an experiment had the following reaction times (in milliseconds). 231, 480, 480, 484, 486, 492, 497, 501, 505, 507, 509 Complete the parts below to identify any outliers. (a) Let Q, be the lower quartile and Q, be the upper quartile of the data set. Find Q, and Q, for the data set. 2₁-0 2₁-0 (b) Find the interquartile range (IQR) of the data set. IQR- (c) Calculate a lov boundary using Q₁-1.5 1QR. Calculate an upper boundary using Q, +1.5-1QR. (Note that 1.5 1QR means 1.5 times the IQR.) Lower boundary: Upper boundary: (d) Any values less than the lower boundary or greater than the upper boundary are considered outliers. Identify all the outliers of the data set. If there is more than one outlier, separate them with commas. If there are no outliers, click "None". Outliers: na NoneIf x represents a random variable with mean 137 and standard deviation 16, then the standard deviation of the sampling distribution of the means with sample size 64 is 2. True O False
- Suppose a simple random sample of size n=64 is obtained from a population with μ=83 and σ=16. (a) Describe the sampling distribution of x. (b) What is P x>86.7? (c) What is P x≤78.3? (d) What is P 80.8<x<86.9?A local DMV (location of your choice) wanted to assess the number of mistakes that were made by its operators (aka clerks). One hundred samples were gathered from each of 20 operators (note: n = 100 for calculation of σp but you will need 100 * 20 to calculate p-bar). The results are shown in the table below. The DMV wants to set control limits to include 95% of the random variation. Operator # Number of errors Fraction defective Operator # Number of errors Fraction defective 1 6 11 6 2 5 12 1 3 0 13 8 4 1 14 7 5 4 15 5 6 2 16 4 7 5 17 11 8 3 18 3 9 3 19 0 10 2 20 4 Calculate p-bar and σp. Complete the fractions defective in chart. Compute the control limits and center line for a p-chart. Plot the fraction defective in a p-chart and decide if the performance of the operators is…Four-year-olds in China average 3 unsupervised hours per day. Most of the unsupervised children live in rural areas, considered safe. Suppose that the amount of unsupervised time is normally distributed with standard deviation 0.5 . A Chinese 4-year-old is randomly selected from a rural area. We are interested in the amount of time the child spends alone per day. In each appropriate box you are to enter either a rational number in "p/q" format or a decimal value accurate to the nearest 0.01 a. (3%) In words, the random variable X in which we are interested is defined by X = (pick one) b. (3%) Find the probability that the child spends less than one hour per day unsupervised. P(X 10) = d. (3%) The 70th percentile of the distribution of unsupervised time is given by P(X < = 0.70 .
- when a population is uniformly distributed (flat), is the sampling distribution of xbar for random samples of 2 observations roughly normal, strongly skewed, or triangular?Out of a sample of 160 girls , 100 preferred FANTA to COKE while a sample of140 boys had 30 preferring COKE to FANTA .At level of significance α = 0.01and without using normal distribution, find out if there is a significant differencebetween the two proportions preferences for FANTASuppose you are constructing a CI for a mean using T distribution and your sample size is 33. What would tge degree of freedom be for the t distribution that you would be using
