Exam 22: Statistical Inference: Conclusion

The irradiation of food to destroy bacteria is an increasingly common practice. In order to determine which one of two methods of irradiation is best, a scientist took a random sample of 100 one-kilogram packages of minced meat and subjected 50 of them to irradiation method 1 and the remaining 50 to irradiation method 2. The bacteria counts were measured and the following statistics were computed. The scientist noted that the data were normally distributed. Method 1 Method 2 =86 =98 =324 =841 Estimate with 95% confidence the mean bacteria count with method 2.

The irradiation of food to destroy bacteria is an increasingly common practice. In order to determine which one of two methods of irradiation is best, a scientist took a random sample of 100 one-kilogram packages of minced meat and subjected 50 of them to irradiation method 1 and the remaining 50 to irradiation method 2. The bacteria counts were measured and the following statistics were computed. The scientist noted that the data were normally distributed. Method 1 Method 2 =86 =98 =324 =841 Can we conclude at the 5% significance level that the variance of the bacteria count with method 2 is less than 1500?

With hypothesis testing, there are only two types of errors: Type I error where we incorrectly reject Ho and Type II error where we incorrectly retain Ho.

Two independent samples of sizes 35 and 40 are randomly selected from two normally distributed populations. Assume that the population variances are unknown but equal. In order to test the difference between the population means, $\mu _ { 1 } - \mu _ { 2 }$ , the sampling distribution of the sample mean difference, $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ , is: A normally distributed. B t -distributed with 75 degrees of freedom. C t -distributed with 73 degrees of freedom. D F -distributed with 34 and 39 degrees of freedom.

The irradiation of food to destroy bacteria is an increasingly common practice. In order to determine which one of two methods of irradiation is best, a scientist took a random sample of 100 one-kilogram packages of minced meat and subjected 50 of them to irradiation method 1 and the remaining 50 to irradiation method 2. The bacteria counts were measured and the following statistics were computed. The scientist noted that the data were normally distributed. Method 1 Method 2 =86 =98 =324 =841 Estimate with 95% confidence the ratio of the two variances.

There are different approaches to fitness training. To judge which one of two approaches is better, 200 25-year-old men were randomly selected to participate in an experiment. For four weeks, 100 men were trained according to approach 1 while the other 100 men were trained according to approach 2. The percentage improvement in fitness was measured for each man and the statistics shown below were computed. The percentage figures are known to be normally distributed. Approach 1 Approach 2 =27.3 =33.6 =47.614 =28.09 a. Estimate with 95% confidence the ratio of the variances of the percentage improvement in fitness, and briefly describe what the interval estimate tells you. b. Do these results allow us to conclude at the 5% significance level that approach 2 is superior?

In a one-tail test, the p-value is found to be equal to 0.0456. If the test had been two-tailed, the p-value would have been 0.0912.

From a sample of 500 items, 30 were found to be defective. The point estimate of the population proportion defective will be: A 0.06 B 30.0 C 16.667 D None of these choices are correct.

In testing the hypotheses: $H _ { 0 } : p = 0.50$ $H _ { 1 } : p \neq 0.50$ , at the 10% significance level, if the sample proportion is 0.56, and the standard error of the sample proportion is 0.025, the appropriate conclusion is: A to reject B not to reject C to reject D to reject both and .

Which of the following best describes a p-value? A A p-value is the probability of getting our population results or more extreme if the null hypothesis about the sample statistic were really true B A p-value is the probability of getting our sample results or more extreme if the null hypothesis about the population parameter were really true C A p-value is the probability of getting our sample results. D A p-value is the probability of getting our sample results or more extreme if the null hypothesis about the population parameter were really false

In testing the difference between two population means using two independent samples, the population standard deviations are assumed to be known and the calculated test statistic equals 1.05. If the test is upper-tail and the 10% level of significance has been specified, the conclusion should be to: A reject the null hypothesis. B not to reject the null hypothesis. C choose two other independent samples. D None of these choices are correct.

A statistics course at a large university is taught in each semester. A student has noticed that the students in semester 1 and semester 2 are enrolled in different degrees. To investigate, the student takes a random sample of 25 students from semester 1 and 25 students from semester 2 and records their final marks (%) provided in the table below. Excel was used to generate descriptive statistics on each sample. Assume that student final marks are normally distributed in each semester. Sample of semester 1 fin al marks 69 45 53 76 53 89 59 63 89 77 49 57 59 60 83 96 83 59 92 67 82 64 62 88 71 Sample of semester 2 fin al marks 49 40 93 58 79 46 82 54 79 59 45 54 87 77 63 81 60 96 53 69 92 69 60 69 54 Semester 1 Mean 65.48 Stan dard Error 2.679 Median 63 Mode 55 Standard Deviation 13.395 Sample Variance 179.43 Range 43 Minimum 45 Maximum 88 Sum 1637 Count 25 Semester 2 Mean 60.96 Standard Error 2.5136 Median 59 Mode 54 Standard Deviation 12.568 Sample Variance 157.96 Range 47 Minimum 40 Maximum 87 Sum 1524 Count 25 Can we conclude at the 5% significance level that the variance of semester 2 student's final marks is greater than 150?

When the necessary conditions are met, a two-tail test is being conducted to test the difference between two population proportions, but your statistical software provides only a one-tail area of 0.03 as part of its output. The p-value for this test will be: A 0.03 B 0.06 C 0.05 D None of these choices are correct.

In testing the null hypothesis $H _ { 0 } : p _ { 1 } - p _ { 2 } = 0$ , if ${ H } _ { 0 }$ is false, the test could lead to: A Type I error. B Type II error. C Either a Type I or a Type II error. D None of these choices are correct.

The lower limit of the 87.4% confidence interval for the population proportion p, given that n = 250 and $\tilde { p }$ = 0.15, is 0.1492.

Descriptive statistics helps us describe and summarise data whereas inferential statistics helps us draw conclusions about populations based on samples of data.

If a sample of size 300 is selected, the value of A for the probability P(-A $\leq$ t_df=n-1 $\leq$ A) = 0.90 is 1.96.

A statistics course at a large university is taught in each semester. A student has noticed that the students in semester 1 and semester 2 are enrolled in different degrees. To investigate, the student takes a random sample of 25 students from semester 1 and 25 students from semester 2 and records their final marks (%) provided in the table below. Excel was used to generate descriptive statistics on each sample. Assume that student final marks are normally distributed in each semester. Sample of semester 1 final marks 65 45 53 76 53 85 55 63 85 77 45 57 55 60 83 96 83 55 52 67 82 64 62 88 71 Sample of semester 2 final marks 45 40 53 58 75 46 82 54 75 59 45 54 87 77 63 81 60 56 53 65 52 65 60 65 54 Semester 1 Mean 65.48 Stan dard Error 2.679 Median 63 Mode 55 Standard Deviation 13.395 Sample Variance 179.43 Range 43 Minimum 45 Maximum 88 Sum 1637 Count 25 Semester 2 Mean 60.96 Standard Error 2.5136 Median 59 Mode 54 Standard Deviation 12.568 Sample Variance 157.96 Range 47 Minimum 40 Maximum 87 Sum 1524 Count 25 Estimate a 95% confidence interval for the difference in final marks between semester 1 and semester 2 students in this statistics course. Assume that the population variances are unknown and equal.

The irradiation of food to destroy bacteria is an increasingly common practice. In order to determine which one of two methods of irradiation is best, a scientist took a random sample of 100 one-kilogram packages of minced meat and subjected 50 of them to irradiation method 1 and the remaining 50 to irradiation method 2. The bacteria counts were measured and the following statistics were computed. The scientist noted that the data were normally distributed. Method 1 Method 2 =86 =98 =324 =841 a. Estimate with 95% confidence the ratio of the variances of the bacteria counts under the two methods, and briefly describe what the interval estimate tells you. b. Do these results allow us to infer at the 5% significance level that there is a difference in bacteria count between methods 1 and 2? c. Do these results allow us to infer at the 5% significance level that the mean bacteria count with method 1 is less than 95?

When the necessary conditions are met, a two-tail test is being conducted to test the difference between two population means, but your statistical software provides only a one-tail area of 0.0327 as part of its output. The p-value for this test will be 0.0654.