A sample of 7 measurments, randomly selected from a normally distributed population, resulted in a sample mean x¯=5.7 and sample standard deviation s=1.68. Using α=0.05, test the null hypothesis that the mean of the population is 4.5 against the alternative hypothesis that the mean of the population is less than 4.5 by giving the following: (a) the degree of freedom (b) the critical ?t value (c) the test statistic The final conclusion is A. We can reject the null hypothesis that μ=4.5. B. There is not sufficient evidence to reject the null hypothesis that μ=4.5.
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A sample of 7 measurments, randomly selected from a
(a) the degree of freedom
(b) the critical ?t value
(c) the test statistic
The final conclusion is
A. We can reject the null hypothesis that μ=4.5.
B. There is not sufficient evidence to reject the null hypothesis that μ=4.5.
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- A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the balls bounce upward to be 54.8 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between −t0.95 and t0.95, then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the sample is 56.3 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls?To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.5 seconds. A random sample of 24 sedans has a mean minimum time to travel a quarter mile of 15.4 seconds and a standard deviation of 2.09 seconds. At α=0.01 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.
- 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 = 5.23. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. O Ho: μ = 5.5 H₂:μ> 5.5 O Ho: μ = 5.5 H₂: μ = 5.5 ⒸHO: μ = 5.5 H₂:μ ≥ 5.5 O Ho: μ = 5.5 H₂: μ< 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. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true verage percentage differs from the desired percentage. O Reject the null hypothesis. There is not sufficient evidence to…Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x, be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x, be the empathy = 68.36. Another random sample of 31 fathers gave score of a father. A random sample of 37 mothers gave a sample mean of x, X, = 60.06. Assume that o, = 11.55 and o, = 11.45. (a) Let u, be the population mean of x, and let u, be the population mean of x,. Find a 99% confidence interval for u, - Hz. (Round your answers to two decimal places.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level? Because the interval contains only…The CSV file modeldata.csv contains 200 observations of 4 explanatory variables (x1, x2, x3, x4) and a response variable (y). A multiple linear regression model is built in R using the following code, > modeldata <- read.csv("modeldata.csv") > x1 <- modeldata$x1 > x2 <- modeldata$x2 > x3 <- modeldata$x3 > x4 <- modeldata$x4 > y <- modeldata$y > model <- lm(y~x1+x2+x3+x4) Question: What this particular plot shows about the model being analysed?Time to Complete the Course Right 45 47 50 49 50 50 48 44 Left | 45 | 43 48 47 50 52 | 44 42 Assume a Normal distribution. What can be concluded at the the a = 0.01 level of significance level of significance? For this study, we should use t-test for the difference between two dependent population means a. The null and alternative hypotheses would be: p1 p2 Ні: p1 p2 b. The test statistic t v v = 1.199 (please show your answer to 3 decimal places.) c. The p-value = [1338 your answer to 4 decimal places.) d. The p-value is > va e. Based on this, we should fail to reject f. Thus, the final conclusion is that ... * (Please show v the null hypothesis. O The results are statistically insignificant at a = 0.01, so there is insufficient evidence to conclude that the population mean time to complete the obstacle course with a patch overSuppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(The NAEP considers that a national average of 283 is an acceptable performance. Using α = .05, run a two-tail t-test for one sample to test Ho: µ=283 for the 2019 scores. Report the t-obt, df, and p-values. Would you reject the null hypothesis that the 2019 scores come from a population with average 283? If this is the case, does it come from a population from larger or smaller average?Claim: The mean pulse rate (in beats per minute) of adult males is equal to 68.8 bpm. For a random sample of 162 adult males, the mean pulse rate is 68.4 bpm and the standard deviation is 11.5 bpm. Complete parts (a) and (b) below. a. Express the original claim in symbolic form. bpm (Type an integer or a decimal. Do not round.) b. Identify the null and alternative hypotheses. Họ: bpm H1: (Type integers or decimals. 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