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- A scientist claims that pneumonia causes weight loss in mice. The table shows the weights (in grams) of six mice before infection and two days after infection. At a=0.05, is there enough evidence to support the scientist's claim? Assume the samples are random and dependent, and the population is normally distributed. Mouse 1 4 6. Weight (before) Weight (after) 20.8 22.4 21.7 23.6 19.6 19.9 20.8 22.5 21.5 23.7 19.5 19.8 1) Find the standardized t test 2) Find the P-value 3) Decide whether to reject or fail to reject the null hypothesis. 4) Interpret the decision in the context of the original claim. 19,600Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (°F). 21.0 15.1 19.0 17.6 17.5 15.5 14.7 17.1 y 87.8 71.4 94.1 84.7 81.4 75.2 69.7 82.0 15.4 16.2 15.0 17.2 16.0 17.0 14.4 69.4 83.3 79.6 82.6 80.6 83.5 76.3 Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answer to four decimal places.) %3D X = y = + %3D Find the value of the coefficient of determination r. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to four decimal places. Round your…Media experts claim that daily print newspapers are declining because of Internet access. Listed below, from left to right and then top to bottom, are the numbers of daily print newspapers in a large region for a recent sequence of years. First find the median, then test for randomness of the numbers above and below the median using a = 0.05. What do the results suggest? 1620 1593 1570 1554 1547 1539 1524 1513 1488 1485 1477 1467 1455 1454 1455 1446 1433 1428 1408 1391 1380 The median is (Type an integer or a decimal. Do not round.) ~
- The shelf life (in days) for bottles of a product is a continuous random variable having the density function 1 ifx>1 f(x)={ x2' 0, else. Let F(x) be the cumulative distribution function for X. Find F(7.85). Round your answer to a number with two decimal digits after the decimal point. For example if your answer is 1/40, which is equal to 0.025, then you should enter 0.03.The data represents the murder rate per 100,000 individuals in a sample of selected cities in the United States. Find the variance and standard deviation. Round your answer to at least one decimal place. class limit Frequency 5-11 9 12-18 5 19-25 8 26-32 3 33-39 3 40-46 7Problem Solving. Solve the following problems. No immediate rounding. Round off final answers to three decimal places. A protective enchantment which alerts the Charms professor when a death eater attacks a magical school is designed to have a 90% reliability rate. Suppose that the nine magical schools equipped with this enchantment experienced an attack from the death eaters. Define the random variable X as the number of Charms professors alerted out of nine. Assuming that protective enchantment alerts are independent 1. Write down the associated PMF of X. 2. Compute for the probability of alerting at least 7 Charms professors.
- A random sample of 30 states shows the number of low-power FM radio stations for each state. Find the variance and standard deviation for the data. Class limits Frequency 1- 9 10 – 18 19 – 27 19 – 27 10 28 – 36 3 37 – 45 3 46 – 54Need help with this Intro to probability and statistics homework problem. Make sure your handwriting is neat and readable.Part 2 Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.338 0.306 0.340 0.248 0.367 0.269 y 3.5 7.7 4.0 8.6 3.1 11.1 Σx = 1.868, Σy = 38, Σx2 = 0.592034, Σy2 = 294.32, Σxy = 11.1556, and r ≈ -0.901. Se ≈ 1.5890, a ≈ 26.420, and b ≈ -64.517. (a) Find the predicted percentage of strikeouts for a player with an x = 0.328 batting average. (Use 2 decimal places.) %(b) Find a 90% confidence interval for y when x = 0.328. (Use 2 decimal places.) lower limit % upper limit %
- Suppose that a manager of a large apartment complex provides the following subjective probability estimates about the number that exists per month. Vacancies Probability 0 .05 1 .15 2 .35 3 .25 4 .10 5 .10 Provide the probability of each of the following events. a. No vacancies b. At least four vacancies c. Two or fewer vacanciesChapter 13 Assignment Hint(s) Check My Work 13 remaining) 2. To study the effect of temperature on yield in a chemical process, fve batches were produced at cach of three temperature levels. The results follow. 4. Temperature 5. 50°C 70°C 34 33 22 6. 24 34 27 36 37 27 39 26 29 32 30 30 Construct an analysis of variance table (to 2 dedmais but p-value to 4 decimals, if necessery). Source of Varlation Sum of Squares Degrees of Freedom Mean Square p-value Truatments Error Total 14 Use a 0.06 level of significonce to best whether the tempereture kvel hes an effect on the mean yiekd of the process. Calcu ate the value of the test stacistic (to 2 decimals). The p-value is batwoon D.01 and 0.02s What is your condlusion? De not reject the unptien thwt the men yieldu for the three bernperstures eequwExploration 4. Assume that 5 students taking a statistics course having the following ages: 17 33 29 20 45 Mean a. Find the mean and population standard deviation of the data set of ages. Standard Deviation b. Assume that random samples of size n = 2 are selected with replacement. Make a list of all of the possible samples of size 2. They are selected with replacement, i.e. the same student could be chosen twice. Also, selecting the age of 17 first and 33 second is different from selecting 33 first and 17 second. You need to make a list of all the possible outcomes (there should be 25.....) Find the mean of each sample and construct a table representing the sampling distribution of the mean.
