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- Suppose you have a sample of size n for variables X and Y. The sample covariance of X and Y is Cov(X,Y) = 1,000, the sample standard deviation for X is Sx=20 and the sample standard deviation for Y is SY=75. What is the sample correlation coefficient, r?The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? = 0.32 and that x = 5.21. (Use ? = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses. H0: ? = 5.5Ha: ? ≠ 5.5H0: ? = 5.5Ha: ? ≥ 5.5 H0: ? = 5.5Ha: ? < 5.5H0: ? = 5.5Ha: ? > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence…A random sample of n = 16 scores is obtained from a population with a mean of μ = 80, and a treatment is administered to the sample. After treatment, the sample mean is found to be M = 82. Assuming the sample variance is s 2 = 1600, what is the estimated d?
- 28 - What is the standard deviation of the frequency series given below? si fi 2 1 4 3 5 5 7 4 9 2 a) 4.00 B) 2.36 NS) 1.95 D) 3.68 TO) 5.56 29 - The distribution of sales of fire extinguishers produced for factories is given below. Find the variance of the distribution. a) 4.34 B) 1.00 NS) 6.28 D) 2.54 TO) 5.46The null and alternate hypotheses are:H0: μ₁ = μ2H1: μ₁ ≠ μ2 A random sample of 10 observations from one population revealed a sample mean of 26 and a sample standard deviation of 5.0. A random sample of 8 observations from another population revealed a sample mean of 30 and a sample standard deviation of 6.0. The population standard deviations are unknown but assumed to be equal. At the 0.01 significance level, is there a difference between the population means?As noted on page 275, when the two population means are equal, the estimated standard error for the indepen- dent-measures t test provides a measure of how much difference to expect between two sample means. For each of the following situations, assume that m1 5 m2 and calculate how much difference should be expected between the two sample means. One sample has n 5 6 scores with SS 5 70 and the second sample has n 5 10 scores with SS 5 140. One sample has n 5 6 scores with SS 5 310 and the second sample has n 5 10 scores with SS 5 530. In Part b, the samples have larger variability (big- ger SS values) than in Part a, but the sample sizes are unchanged. How does larger variability affect the magnitude of the standard error for the sample mean difference?
- Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.A single thermometer is randomly selected and tested. Let ZZ represent the reading of this thermometer at freezing. What reading separates the highest 15.55% from the rest? That is, if P(z>c)=0.1555P(z>c)=0.1555, find c.c=c= °CA truck company decides that every year, the distance traveled for the truck usually distributed normally with average traveled 50.0 thousands miles and the standart deviation os 12.0 thousands miles Questions A. How many of the 1,000 trucks in the fleet are expected to cover between 30.0 and 60.0 thousand miles this year B. How many miles will at least 80% of the trucks travel C. How many of the 1,000 trucks in the fleet are expected to cover between 30.0 and 60.0 thousand miles this year, if the standart deviation is changed to 10 thousands milesYou source a battery for your product from two different suppliers (A and B). You suspect that theequivalent series resistance (ESR) of batteries supplied by the two suppliers is not the same. Thestandard deviation of ESR from each supplier is 2 ohms. You would like to be able to determine an ESRdifference of 1 ohms between suppliers. How many parts would you need to sample from each supplier(assume you sample the same number from each supplier) for a power level of 90%. Assume the desiredsignificance level (?) is 5%.
- The effectiveness of a new bug repellent is tested on 1616 subjects for a 10 hour period. (Assume normally distributed population.) Based on the number and location of the bug bites, the percentage of surface area exposed protected from bites was calculated for each of the subjects. The results were as follows: ?⎯⎯⎯=92x¯=92, ?=13 s=13 The new repellent is considered effective if it provides a percent repellency of at least 9090. Using ?=0.05α=0.05, construct a hypothesis test with null hypothesis ?≤90μ≤90 and alternative hypothesis ?>90μ>90 to determine whether the mean repellency of the new bug repellent is greater than 9090 by computing the following: (a) the degree of freedom (b) the test statistic The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that ?≤90μ≤90. Our results do not provide enough evidence that the new bug repellent is effective. B. We can reject the null hypothesis that ?≤90μ≤90. Our results indicate that…The weights of radish seeds are normally distributed, with µ = 0.12 g and σ = 0.02 g. What is the z-score of a radish seed that weighs 0.093 g? If the contents of a seed packet weighs 30.0 g, approximately how many seeds are in it? Approximately how many seeds in the packet weigh between 0.08 g and 0.16 g.?