655 topic 3 disc

A transport company wants to compare the fuel efficiencies of the two types of lorry it operates. It obtains data from samples of the two types of lorry, with the following results: Type Average mpg Standard deviation Sample size A B 31.0 32.2 7.6 6.8 33 40 Test the hypothesis that there is no difference in fuel efficiency, using the 95% confidence level.

16 The margin of error for a 95% confidence interval for β₁ is, a 1.0045           b 1.0574           c 1.1130           d 1.1716

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A study compared grade point averages (GPA) for students in a class: students were divided by 6 locations where they usually sat during lecture (i.e. left or right front, left or right center, left or right rear). A total sample size of 12 students was studied (2 students from each section) using one-way analysis of variance. i. The sum of squared errors is SSE = 50. What is the value of the Mean Square Error (MSE )? 08.33 04.17 ONone of these O10.00 ii. The sum of squares for location is SSX= 60. What is the Mean Square for X(MSX )? O12 O10 O30 ONone of these

You are the manager of a restaurant for a fast-food franchise. Last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.9 minutes. You select a random sample of 64 orders. The sample mean waiting time is 3.63 minutes, with a sample standard deviation of 0.8 minute. Complete parts (a) and (b) below. ..... a. At the 0.05 level of significance, is there evidence that the population mean waiting time is different from 3.9 minutes? State the null and alternative hypotheses. Ho: H (Type integers or decimals.)

25 An economist would like to test the hypothesis that the average daily screen time that a person spends on mobile devices is greater than 300 minutes. A random sample of 30 smartphone users was selected and their daily screen time was recorded. The standard deviation for the 30 smartphone owners using their devices is 112.19 minutes and the sample mean of the daily screen time is 297.17 minutes. Using a = 0.05, the test statistic of the sample mean is -1.38 -0.138. 0.138 O 1.38

Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19th century. It is from this study that the name "regression" originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship: Studen th = 19.6 + 0.73 × Midparh, R2 = 0.45, SER = 2.0 (7.2) (0.10) where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. Interpret the estimated slope coefficient and intercept coefficient. What is the meaning of the regression R2 ? What is the prediction for the height of a child whose parents have an average height of 70.06 inches? a. b. с. d. What is the interpretation of the SER here? Is the slope coefficient statistically significantly different from zero (at the 5% significance level)? e.

A statistics instructor is interested in the ability of students to assess the difficulty of a test they have taken. This test was taken by a large group of students, and the average score was 78.5. A random sample of eight students was asked to predict this average score. Their predictions were as follows:72 83 78 65 69 77 81 71Assuming a normal distribution, test the null hypothesis that the population mean prediction would be 78.5. Use a two-sided alternative and a 10% signifi- cance level.

Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression: TestScore = 520.4 – 5.82 × CS, R² = 0.08, SER = 11.5. a. The sample average class size across the 100 classrooms is 21.4. What is the sample average of the test scores across the 100 classrooms? b. What is the sample standard deviation of test scores across the 100 classrooms?

You estimated the following relationship between the annual salary (S) and the length of employment in the retail sector (LEmp), using a large sample. Salary is measured in dollars and Length of employment in years. The results are as follows: Ŝ; = 23, 005 + 1, 534.4LEmpi i (6,450.8) (524.5) where the appropriate standard errors of the estimators are given in parentheses. The 99% confidence interval for the slope is approximately: O [183.4, 2885.4] [1009.9, 2058.9] O [506.4, 2562.4] O [671.7, 2397.1]

Next 3 questions are related to the following: A random sample of 1200 vehicles on a freeway are clocked to test the hypothesis that the proportion of vehicles driving above 80 miles per hour is 25%. The number of vehicles in the sample driving above 80 mph is 326. What is the sample proportion? 31 a 0.267 0.272 0.276 d 0.281 32 The test statistic is: a 1.73 1.67 1.60 d 1.54 33 The p-value is, 0.0830 Reject Ho at a = 0.10. 0.0798 Do not reject Ho at a = 0.05. 0.0415 Reject Ho at a = 0.05. 0.0399 Reject Ho at a = 0.05. a b d

The management of a soft drink company is interested in determining whether the proper amount of soft drink has been placed in 1-liter bottles at the local bottling plant. The bottling plant has informed the management that the population standard deviation for 1-liter bottles is 0.025 liter. A random sample of 100 1-liter bottles selected from this bottling plant indicates a sample mean of 0.995 liters. Use a one-sample hypothesis test to decide whether the mean amount in the bottles is different from 1.0 liters. Use a 0.05 level of significance.   State the null and alternative hypothesis for this problem. Determine the sample test statistic value for this problem. Determine the critical test statistic value for this problem. What is your statistical decision for this problem?

Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19th century. It is from this study that the name "regression" originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship: Studenth=19.6+ 0.73x Midparh, R²=0.45, SER=2.0 (7.2) (0.10) where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. (Following Galton's methodology, both variables were adjusted so that the average female height was equal to the average male height.) For the following questions except (d), type your answers in two decimal places. (a) If we test for the statistical significance of the slope coefficient, the relevant f-statistic is t = (b) Construct a 95% confidence interval for a one inch increase in the average of parental height: ( (c)…

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. If α = 0.05, what is the critical t value? 2) A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. what is the degree of freedom

what is the p value？

A national random sample of 20 ACT scores from 2010 is as follows: (29, 26, 13, 23, 23, 25, 17, 22, 17, 19, 12, 26, 30, 30, 18, 14, 12, 26, 17, 18). Calculate the sample mean and standard deviation. Assuming that the ACT is normally distributed, what is the 95% confidence interval for the population ACT score. Group of answer choices 18.25 to 23.45 15.32 to 23.05 19.52 to 22.19 14.32 to 23.15

Grace Floral Shop claims that their average daily earnings is $497. An auditor wants to determine whether this claim is true. The auditor randomly selected a sample of 100 days and found that the sample mean earnings was $495 with a sample standard deviation of 9.75. Calculate the 97% confidence interval for the population mean daily earning.   Assist the auditor in conducting a hypothesis test, at the 3% level of significance, to determine whether the claim about their average daily earnings was overstated. State the null and the alternative hypothesis for this test. Using the p-value approach, state the decision rule for this Calculate the value of the test statistic for this test. Calculate the p-value for this test? State the conclusion of this test. Give reason for your

The sum of squared residuals for the first group (SSR1) is 15.3 and for the second group (SSR2) is 25.7. Each group contains 12 observations after removing the central observations and this model has only one independent variable. Calculate the F-statistic (rounded to two dp) (a) 2.57 (b) 2.41 (c) 1.92 (d) 1.68 (e) 1.67

You have a regression: Ý 0.42 + 0.9 X₁ - 1.37X2 +0.61X3 (0.24) (0.5) (0.34) N = 50, R² = 0.67 What is the test statistic for Ho: B2 B3 B4 = 0 v.s. H₁ at least one of them is not zero. 28.71 31.13 31.8 46.7

1) A researcher estimates an​ AR(1) with an intercept and finds that the OLS estimate of β1 is​ 0.95, with a standard error of 0.02. Does a​ 95% confidence interval include β1=1​?   A.​Yes, since the value of the t​-statistic for the null hypothesis β1=1 is −2.50 and the​ 5% critical value of the augmented​ Dickey-Fuller statistic is −​2.86, the null hypothesis is not rejected. Thus β1=1 is in the​ 95% confidence interval.   B.​No, the​ interval, calculated as β1±1.96SEβ1​, is from 0.91 to 0.99.   C.​No, since the value of the t​-statistic for the null hypothesis β1=1 at the​ 5% level is −2.50.   D.​No, because the critical value of the augmented​ Dickey-Fuller statistic at the​ 5% significance level is −2.86.

A random sample of residents from various income brackets was asked their opinion on tax reform for the country of Guyana. The data so gathered were analyzed by a statistician and the results he obtained using MINITAB are shown below:   Expected counts are printed below observed counts     Low Middle High Total For 26 (30.67) 75 (51.11) 14 (33.22) 115 Against 60 (69.33) 95 (115.56) 105 (**) 260 Neutral 34 (20) 30 (33.33) 11 (21.67) 75 Total * 200 130 450 Chi-sq = 0.71 + 11.17 + 11.12 +     *** + 3.66 + 11.89 +     9.8 + 0.33 + 5.25 = 55.2 DF =??, p-value =???   Carefully define the null and alternative hypotheses of the x2 test underlying the generation of the above table.  Find the missing values ‘*’, ‘**’, ‘***’, ‘??’ and ‘???’. What is the conclusion of this test? Give reasons for your answer.

In regression model: Yi = B1+ B2Xi+ Ei, where Ei is a random variable independent of Xi, with mean and variance constant and different from zero. Ei ~(media, varianza) Obtain the OLS estimator of ẞ2. Show that the properties of finite samples hold.

the regression R2 is 0.98.This mean

Question 2 In 2015, the average duration of long-distance telephone calls from a certain town was 3.9 minutes. A telephone company wants to perform a test to determine whether this average duration of long- distance calls has changed. Fifty calls, originating from the town, was randomly selected and the following summary minutes. Σx= 205 E(x - x)? = 56.43 a) Calculate the sample mean, &. b) Calculate the sample standard deviation c) Using the p value approach at the 1% level of significance, test whether the mean duration of long-distance calls from the town had increased. d) Construct the 99% confidence interval for the population mean duration of the long-distance calls from the town.

The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean weight of 4.8 ounces with a sample standard deviation of 0.3 ounces. At the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is less than 4 ounces.   The correct conclusion at the 0.05 level of significance is ________________________ .   a.   reject the null hypothesis; evidence suggests that the mean weight is less than 4 ounces   b.   do not reject the null hypothesis   c.   do not reject the null hypothesis; evidence suggests that the mean weight is less than 4 ounces   d.   reject the null hypothesis   e.   evidence suggests that the mean weight is less than 4 ounces