A normal population has mean u (unknown) and variance 0.018. A random sample of size 20 observations has been taken and its variance is found to be 0.024. Test the null hypothesis H,: ở = 0.018 against H,: o < 0.018 at 5% level of significance.
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- An electronic company's records show that the mean number of circuit.boards rejected per batch is 5.7 with a variance of 1.4. Due to a change in the molding process, factory management has hired you to perform a hypothesis test to check if the variance, o, has increased. To do so, you test a random sample of 10 batches produced using the new process; the number of circuit boards rejected per batch has a sample variance of 2.5. Under the assumption that the number of circuit boards rejected per batch using the new process follows a normal distribution, you will perform a chi-square test. Find x, the value of the test statistic for your chi-square test. Round your answer to three or more decimal places. * = 0The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers? Use α = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal. Teacher 1 Teacher 2 ?̅1 = 473 ?̅2 = 459 S1 = 39.7 S2 = 24.5 n 1 = 8 n 2 = 18 a. State the null and alternate hypotheses (write it mathematically) and write your claim. b. Find the test statistic c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and…A random sample of 10 subjects have weights with a standard deviation of 10.5816 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.
- Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.6 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 1313 samples is 7.2 ppm with a variance of 0.49 Assume the population is normally distributed. A level of significance of 0.02 will be used. Make the decision to reject or fail to reject the null hypothesis.A random sample of 10 subjects have weights with a standard deviation of 11.9848 kg . What is the variance of their weights ? Be sure to include the appropriate units with the result .A researcher wonders whether the recession has changed variability in family size in his city. Before the recession, the mean was 3.7 and the standard deviation was 1.76. The researcher randomly selects 41 families from a population that is normally distributed. His sample has a mean of 3.1 and a standard deviation of 1.45. Test the claim that the standard deviation in size has changed at the αα=.05 significance level.
- The data from an independent-measures research study produce a sample mean difference of 4 points, and each sample has a variance of 10. If there are n = 20 scores in each sample, then what is the estimated standard error of the difference between means?An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 260 engines and the mean pressure was 4 lbs/square inch. Assume the variance is known to be 0.64. If the valve was designed to produce a mean pressure of 4.1 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.A study was conducted to compare to brands of milk. Random sample A of 25 packs of milk with a mean content of 237 grams and standard deviation of 8.56 grams. Another sample B of 20 packs of milk showed a mean content of 240 grams and standard deviation of 9.75 grams. Using 0.05 level of significance will we agree that sample A exceeds that of sample B by 2 grams nutrient content, conduct hypothesis testing assuming that variances are equal.
- The mean fineness of yarn is expected to be greater than the standard value of 5 units. To test this claims, the factory graded 16 specimens of the yarn and found the sample mean to be 5.9 units. Assume that the measurement of fineness is normally distributed with a variance of 4.0. We can state (exactly one option is correct) The p-value is 0.1632 and there is strong evidence that the mean exceeds by 5 units at 17% level of significance. The p-value is 0.0002 and there is strong evidence that the mean exceeds 5 units at 1% level of significance. The p-value is 0.3264 which indicates the data are consistent with a mean of 5 units at 35% level of significance.To evaluate the effect of a treatment, a sample is obtained from a population with a mean of =40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 44.5 with a variance of s² = 36. If the sample consists of n = 16 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with a = .05? O For these data, t= 1.50. This value is less than the critical value of 2.131, so we reject the null hypothesis and conclude that there is a significant treatment effect. O For these data, t = 3.00. This value is greater than the critical value of 2.131, so we reject the null hypothesis and conclude that there is a significant treatment effect. O For these data, t = 4.50. This value is greater than the critical value of 2.131, so we reject the null hypothesis and conclude that there is a significant treatment effect. O For these data, t = 1.50. This value is less than the…A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 61 doors is made, and it is found that they have a mean of 2044 millimeters with a variance of 729. Is there evidence at the 0.05 level that the doors are either too long or too short? State the null and alternative hypotheses for the above scenario.