From the scores in subject EQT203 for 8 students, it was found that the mean score is 73 and the standard deviation is 5.15. Construct a 95% confidence interval estimate for the mean score of all students in the class. Ans: (68.69, 77.31)
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- A study of a local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 58 students in the high school and found a mean savings of 4300 dollars with a standard deviation of 600 dollars. Determine a 95% confidence interval for the mean, rounding all values to the nearest whole number.The pH of rain, measured at a weather station in Michigan, was observed for 39 consecutive rain storms. The sample mean is 4.6982 and the sample variance is 0.39623. Obtain a 99% confidence interval for the mean pH of the population of storms at that location.The mean BMI in patients free of diabetes has been reported as 27.8. An investigator measured BMI in 12 patients who are free of diabetes and found a mean BMI of 30.2 with a standard deviation of 5.5. The investigator hypothesizes that the BMI in patients free of diabetes is higher than what has been reported. Is there evidence that the BMI is significantly higher that 27.8? Use a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUSTshow your work to receive full credit. Partial credit is available.
- An SRS of 27 students at NYU gave an average height of 5.4 feet and a standard deviation of .1 feet. Find a 90% confidence interval for the mean height of students at NYU.The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37. Construct a 95% two-sided confidence interval for the standard deviationFind the critical t value to use in making an 80% confidence interval for a mean if the sample size is 35. Write your answer with 3 decimal places.
- A study of a local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 42 students in the high school and found a mean savings of 3800 dollars with a standard deviation of 600 dollars. Determine a 95% confidence interval for the mean, rounding all values to the nearest whole number.Do men take a different amount of time than women to get out of bed in the morning? The 54 men observed averaged 4.3 minutes to get out of bed after the alarm rang. Their standard deviation was 1.4. The 59 women observed averaged 5 minutes and their standard deviation was 2.8 minutes. What can be concluded at the a = 0.01 level of significance? a. For this study, we should use t-test for the difference between two independent population means b. The null and alternative hypotheses would be: Ho: μ1 = + μ2 (please enter a decimal) H₁: μ1 # ♦ μ2 (Please enter a decimal) (please show your answer to 3 decimal places.) c. The test statistic t = d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is α f. Based on this, we should fail to reject + the null hypothesis.On the Stanford-Binet test, the mean IQ is 100. A class of 21 kindergarten pupils were tested with a resulting mean of 92 and a standard deviation of 6.92. What is the standard error of the 90% confidence interval of the average IQ of the kindergarten pupils?
- In a randoms sample of six people, the mean driving distance to work was 19.7 miles and the standard deviation was 6.1 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean u. Interpret the results.An EQ Test was administered to random sample of 130 grade school pupils. The sample mean was 95.8 with standard deviation of 10. Find 99% confidence interval.A random sample of 500 observations yields x̅ =400 and s=50. What is the 95% confidence interval for the population mean?