Compute the standard error of the statistic xˉ1−xˉ2x.
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Researchers are trying to determine if there is a difference in the average lifespan of two species of fruit fly: Ceratitis capitata and Drosophila melanogaster. They measure the lifespans of two random samples of each species. The SRS of Ceratitis capitata was of size 105 and had an average lifespan of 51 days with a standard deviation of 7 days. The SRS of Drosophila melanogaster was of size 95 and had an average lifespan of 48 days with a standard deviation of 6 days.
let μ1 denote the mean lifespan of Ceratitis capitata and μ2 denote the mean lifespan of Drosophila melanogaster.
Compute the standard error of the statistic xˉ1−xˉ2x. Round your answer to four decimal places.
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- A researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 16 blue crabs from Location A contain a mean of 192 milligrams of fish and a standard deviation of 37 milligrams. The stomach contents of a sample of 11 blue crabs from Location B contain a mean of 189 milligrams of fish and a standard deviation of 45 milligrams. At α=0.01, can you support the researcher's claim? Assume the population variances are equal. Complete parts (a) through (d) below.A new computer chip design(A) is being compared to the current design(B).Fifty independent chips of each design are tested for speed at performing a certain task. The new computer chip (A) performed the task in 481.2 ms, on average, with a sample standard deviation of 14.3 ms. The current computer chip (B) performed the task in 495.6 ms, on average, with a sample standard deviation of 16.4 ms. Can you conclude, at a 5% significance level, that chip A performs this task faster than chip B?For a new study conducted by a fitness magazine, 220 females were randomly selected. For each, the mean daily calorie consumption was calculated for a September-February period. A second sample of 260 females was chosen independently of the first. For each of them, the mean daily calorie consumption was calculated for a March-August period. During the September-February period, participants consumed a mean of 2385.8 calories daily with a standard deviation of 218. During the March-August period, participants consumed a mean of 2414.2 calories daily with a standard deviation of 267.5. The population standard deviations of daily calories consumed for females in the two periods can be estimated using the sample standard deviations, as the samples that were used to compute them were quite large. Construct a 90% confidence interval for −μ1μ2, the difference between the mean daily calorie consumption μ1 of females in September-February and the mean daily calorie consumption μ2 of females…
- A researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 14 blue crabs from Location A contain a mean of 194 milligrams of fish and a standard deviation of 37 milligrams. The stomach contents of a sample of 8 blue crabs from Location B contain a mean of 184 milligrams of fish and a standard deviation of 44 milligrams. At a = 0.05, can you support the researcher's claim? Assume the population variances are equal. Complete parts (a) through (d) below. (a) Identify the null and alternative hypotheses. Choose the correct answer below. ОА. Но H1-H2 0 OD. Ho: H₁-12₂=0 Ha H1 H₂0 enough evidence at the 5% level of significance to support the researcher's claim.A researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 13 blue crabs from Location A contain a mean of 191 milligrams of fish and a standard deviation of 37 milligrams. The stomach contents of a sample of 7 blue crabs from Location B contain a mean of 185 milligrams of fish and a standard deviation of 41 milligrams. At α=0.10, can you support the researcher's claim? Assume the population variances are equal and that both samples are from normal populations. Complete parts (a) through (d) below. (a) Identify the null and alternative hypotheses. Choose the correct answer below. A. H0: μ1−μ2=0 Ha: μ1−μ2>0 B. H0: μ1−μ2<0 Ha: μ1−μ2=0 C. H0: μ1−μ2=0 Ha: μ1−μ2≠0 D. H0: μ1−μ2=0 Ha: μ1−μ2<0 (b) Calculate the test statistic t=? (Round to three decimal places as needed.) (c) Calculate the…Bone mineral density (BMD) is a measure of bone strength. Studies show that BMD declines after age 45. The impact of exercise may increase BMD. A random sample of 59 women between the ages of 41 and 45 with no major health problems were studied. The women were classified into one of two groups based upon their level of exercise activity: walking women and sedentary women. The 39 women who walked regularly had a mean BMD of 5.96 with a standard deviation of 1.22. The 20 women who are sedentary had a mean BMD of 4.41 with a standard deviation of 1.02. Which of the following inference procedures could be used to estimate the difference in the mean BMD for these two types of women
- Researchers are trying to determine if there is a difference in the average lifespan of two species of fruit fly: Ceratitis capitata and Drosophila melanogaster. They measure the lifespans of two random samples of each species. The SRS of Ceratitis capitata was of size 105 and had an average lifespan of 51 days with a standard deviation of 7 days. The SRS of Drosophila melanogaster was of size 95 and had an average lifespan of 48 days with a standard deviation of 6 days.Urgent help needed pleaseKing Tut was an ancient Egyptian ruler whose tomb was discovered and opened in 1923 . Legend has it that the archaeologists who opened the tomb were subject to a "mummy's curse," which would shorten their life spans. A team of scientists conducted an investigation of the mummy's curse. They reported that the 24 people exposed to the curse had a mean life span of 71.1 years with a standard deviation of 11.6 years, while a sample of 12 Westerners in Egypt at the time who were not exposed to the curse had a mean life span of 77.7 years with a standard deviation of 13.9 years. Assume that the populations are approximately normal. Can you conclude that the mean life span of those exposed to the mummy's curse differs from the mean life span of those not exposed? Let μ1 denote the mean life span of those exposed to the mummy's curse and μ2 denote the mean life span of those not exposed. Use the =α0.01 level and the P -value method with the TI-84 Plus calculator. do we…
- The owners of the Metro Cash & Carry wished to study customers’ shopping habits. From earlier studies, the owners were under the impression that a typical shopper spends 0.7 hour at the mall, with a standard deviation of 0.10 hour. Recently the owners added some specialty restaurants designed to keep shoppers in the mall longer. A research team was hired to evaluate the effects of the restaurants. A sample of 45 shoppers by the team revealed that the mean time spent in the mall had increased to 0.80 hour. i. Develop a hypothesis test to determine if the mean time spent in the mall changed. Use the .10 significance level. ii. Suppose the mean shopping time actually increased from 0.75 hour to 0.79 hours. What is the probability of making a Type II error? iii)When research team reported the information in part (b) to the mall owners, the owners believed that the probability of making a Type II error was too high. How could this probability be reduced? plz sove it…A study was conducted in which mice that had a dim light on at night (rather than complete darkness) ate most of their calories when they should have been resting. These mice gained a significant amount of weight, despite eating the same number of calories as mice kept in total darkness. The time of eating seemed to have a significant effect. There were 10 mice in the group with dim light at night and they gained an average of 7.9 g with a standard deviation of 3.0. We see in Figure 1 that the data are not heavily skewed and do not have extreme outliers. 00 O O 2 4 8 10 12 14 BM Gain Figure 1 Body mass gain (in grams) for mice with a night light Use the t-distribution to find a 90% confidence interval for weight gain. Round your answers to two decimal places. The 90% confidence interval is i to i !A researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 13 blue crabs from Location A contain a mean of 191 milligrams of fish and a standard deviation of 38 milligrams. The stomach contents of a sample of 8 blue crabs from Location B contain a mean of 189 milligrams of fish and a standard deviation of 44 milligrams. At a = 0.10, can you support the researcher's claim? Assume the population variances are equal. Complete parts (a) through (d) below. t= 0.110 (Round to three decimal places as needed.) (c) Calculate the P-value. P=|| (Round to four decimal places as needed.)