(a) Suppose a random sample of size n= 25 from a normal population with unknown variance has sample mean = 50 and sample variance s2 = 64. Construct a 100(1-a)% Confidence Interval (C.I.) for the population mean u with a = 0.10, a = 0.05 and a = 0.01. )Find the lengths of the intervals constructed above. What is the relationship between the confidence level (1-a) and the length of C.I.?
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- A scientist wants to establish if the Mississippi’s river height has increased using data from 1970 and 2020. Historically, it’s known that the variance of the height within any given year is 4.5ft. The sample from 1970 has 80 measurements with ?1μ1 = 30ft and the sample from 2020 has 260 measurements with ?2μ2 = 31.5ft. Find a 95% confidence interval for the average increase of height.is 0.80 against the alternative that it is not. (Simple Regression & Correlation] 06. (a) Duracell manufactures batteries that the CEO claims will last an average of 300 hours under normal use. A researcher randomly selected 20 batteries from the production line and tested these batteries. The tested batteries had a mean life span of 270 hours with a standard deviation of 50 hours. Do wehave enough evidence to suggest that the claim of an average li fetime of 300 hours is false? b) Newborn babies are more likely to be boys than girls. A random sample found 13,173 boys were born among 25,468 newbom children. The sample proportion of boys was 0.5172. Is this sample evidence that the birth of boys is more common than the birth of girls in the entire population? Ilypothesis TestingThe mg of nicotine in menthol cigarettes is normally distributed and a sample of 25 menthol cigarettes had a standard deviation of 0.24 mg of nicotine. We will be constructing a 90% confidence interval containing the population variance. The left hand critical value is . Round to 3 decimal places. The right hand critical value is . Round to 3 decimal places. The true variance of the mg of nicotine found in menthol cigarettes is in the interval ( , ). Round your answers to 3 decimal places.
- Construct a 90% confidence interval for H₁-H2 with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances. Stats x₁ =99 mg, s₁ = 3.93 mg, n₁ = 18 X280 mg, s2 = 2.02 mg, n₂ = 9 Confidence interval when (x-x2)-tc variances are not equal 01 + $2 < ոշP.v.n.g5. An experiment was conducted to compare the vinegar content of salad dressing on two different production lines. Production was monitored 10 times a day. The data are shown here. For Production line 1, the sample variance si= 2.0, for the production line 2, the sample variance s = 0.4. Find a 98% confidence interval for oi/o. Next ousA sample of n=41n=41 data values randomly selected from a normally distributed population has variance s2=30s2=30. Construct a 95% confidence interval for the population variance. Round your endpoints to one decimal place.An experiment is replicated to determine the variation in temperature for which a certain process takes place. Six readings were obtained and recorded in units of Kelvin. The readings recorded were 371.5, 370.3, 370.6, 371.2, 370.8 and 369.2. (i) (ii) Construct a 95% confidence interval for the true variance in temperatures. As a result obtain a 95% confidence interval for the true standard deviations in temperatures.The difference in the Organic Chemistry final exam scores between last semester and three years ago will be analyzed by the dean. Although the standard deviations of these populations are unknown, the dean has evidence that they are equal. A sample of 41 of these scores from last semester had a mean of 63.7 and standard deviation of 4.6, and a sample of 37 scores from three years ago had a mean of 64.7 and standard deviation of 5. A claim is made that the mean final exam score from last semester ( 1) is less than the mean final exam score from three years ago (2). For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t=" before your answers. Round each of your answers to 3 places after the decimal point. 1 (a) Calculate the value of the test statistic used in this test. Test statistic's value= (b) Use your calculator to find the P-value of this test. P-value = 0.180 F3 Submit Question 4 R F4 H % 5 T Q F5 A 6 Y F6 & 7 U F7 * PrtScn 8 F8…Construct a 90% confidence interval for u, - Ho with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances. Stats X = 122 mg, s, = 3.72 mg, n, = 12 X2 = 51 mg, s, =2.17 mg, n2 = 14 %3D %3D Confidence interval when (X1 – X2) -t variances are not equalLet x represent the number of mountain climbers killed each,year. The long-term variance of x is approximately o Suppose that for the past 12 years, the variance has been s = 118.3. = 136.2 Use a 1% level of significance to test the claim that the recent variance for number of mountain-climber deaths is less than 136.2 Find a 90% confidence interval for the population variance. (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom?If a random sample of size n = 20 from a normal population with the variance o = 25 has the mean F = 64.3, construct a 95% confidence interval for the population mean H. %3D %3DSEE MORE QUESTIONSRecommended textbooks for youGlencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillGlencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill