Question

find the critical value . round to three decimal place.

find the standard deviation of the paired differences. round to one decimal place.

construct 99% confidence interval. round to one decimal place.

A state legislator wants to determine whether his voters' performance rating (0-100) has changed from last year to this year. The following table shows the legislator's performance from the same ten randomly selected voters for last year and this year. Use this data to find the 99 % confidence interval for the true difference between the population means. Let d = (this year's rating)-(last year's rating). Assume that the populations of voters' performance ratings are normally distributed for both this year and last year. Rating (last year) 62 67 82 84 94 53 64 49 Rating (this year) 53 89 85 91 66 71 49 44 50 52 80 45 Copy Data Step 1 of 4: Find the mean of the paired differences, d. Round your answer to one decimal place.

find the standard error of the sampling distrubution used in confidence interval. round to the nearest whole number.

construct 90% confidence interval. round to nearest whole number

Answer 1

1.

2.

Let à denotes the sample mean of difference, s denotes the sample standard deviation of difference and n denotes the sample size. Here, 17.4560 d = -4.400, så 304.7111, sd = 17.4560, n = 10, standard error of mean = ✓n Sd = 5.520064 V10 The margin of error is Sd 17.4560 ME *t 1-0.99 * +0.005,9 17.4560 * 3.249836 = 17.939302 17.939 ✓10 ,9 ✓n 2 V10 a 99 percent confidence interval for the population mean of difference ud is Sd =ă *+1.00 1-0.99 ,9 ✓n 17.456 = -4.400 + *t0.005,9 V10 17.456 = -4.400 + * 3.249836 V10 = -4.400 + 17.939302 = (–22.339302, 13.539302) (-22.34, 13.54)

Here, 21 = 1054.000, $1 = 28.0000, n1 = 19, 22 = 1161.000, 32 = 35.0000, n2 = 11 and associated degrees of freedom sz ni 12 df = G+ G = 18 + n-1 n2-1 The Standard error is 28.002 SEN + + 35.002 11 12.354 ni n2 19 The critical value is tcritical = t 1-0.9 ,18 =t0.05,18 = 1.734064 1.734 The margin of error is 31 28.002 28.002 ME = $10.9,18 * t0.050,18 * + 35.002 11 = 1.734 * + 35.002 11 = 21.423006 21.423 ni n2 19 19 a 90 percent confidence interval for the differnce in population means (Mi - U2 ) is = či - 02 + *t 1-0.900 ,18 ni n2 = 21 - 22 ME = (1054.000 – 1161.000) = 21.423006 = -107.000 + 21.423006 = = (-128.423006, –85.576994) ~(-128, -86)