Based on a sample of n = 26, the least-squares method was used to develop the prediction line Y, = 4 + 5X,. In addition, Syx = 1.8, X= 9, and (X -X)2 = 26, Complete parts (a) and (b) below. i=1 Click here for page 1 of critical values of t. Click here for page 2 of critical values of t. a. Construct a 95% confidence interval estimate of the population mean response for X = 5. 26.0036 sHyx = 5s 31.9964 (Round to four decimal places as needed.)
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- A random sample of 50 students was asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 0.83 and the sample kurtosis was 3.98. Test at the 10% level the null hypothesis that the population dis- tribution of amounts spent is normal.1. What does it imply if if more values are concentrated above the mean? (Skewness) And would the value of skewness be less than, greater than, or equal to 0? 2. In case the data is highly skewed, can we still rely on the kurtosis coefficient? Why or why not? 3. Can the z-score be a real measure of dispersion?In Galton’s height data (Figure 7.1, in Section 7.1), the least-squares line for predictingforearm length (y) from height (x) is y = −0.2967 + 0.2738x.a) Predict the forearm length of a man whose height is 70 in.b) How tall must a man be so that we would predict his forearm length to be 19 in.?c) All the men in a certain group have heights greater than the height computed in part(b). Can you conclude that all their forearms will be at least 19 in. long? Explain.
- Based on a sample of n=30,the least-squares method was used to develop the prediction line Yi=4+5Xi. In addition, SYX=3.2, X=7, and ∑i=1nXi−X2=30.Complete parts (a) and (b) below. a. Construct a 95% confidence interval estimate of the population mean response for X=3. ? ≤μY|X=3≤ ? (Round to four decimal places as needed.) b. Construct a 95% prediction interval of an individual response for X=3. ? ≤YX=3≤ ? (Round to four decimal places as needed.) Find the critical value, the computed t-value, and whether to reject or accept the null hypothesis.Suppose a linear model y=β0+β1xy=β0+β1x is fit to a sample data set, and a test of the null hypothesis H0:β1=0H0:β1=0 against an alternative hypothesis HA:β1≠0HA:β1≠0 is performed; a PP-value of 0.4203 is obtained. Which of the following scatter plots depicts the data set on which this model was fit and the hypothesis test was performed?
- Find the critical value, z0, from the z table for the given parameters. a=0.20 two tailed testWhen we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?In the manufacture of synthetic fiber, the fiber is often “set” by subjecting it to high temperatures. The object is to improve the shrinkage properties of the fiber. In a test of 23 yarn specimens, the relationship between temperature in °C (x) and shrinkage in % (y) was summarized by the least-squares line y = −12.789 + 0.133x. The total sum of square was ∑ni=1(yi−y⎯⎯)2∑i=1n(yi−y¯)2 = 57.313, and the estimated error variance was s2 = 0.0670. Compute the coefficient of determination r 2. Round the answer to three decimal places.
- See the attached image for the introduction. In terms of variables xi and parameters βi, write the null and alternative hypotheses for testing whether, after including Price/Square Feet(x2) in the model already, the further incorporation of the other 2 explanatory variables (x1, x3) adds any useful information for explaining pricey. Also, give the value of the F statistic and its degrees of freedom (df).The test statistic of z=−2.31 is obtained when testing the claim that p=1/2. a. Using a significance level of α=0.05,find the critical value(s). b. Should we reject H0 or should we fail to reject H0?An urban community wants to show that the incidence of breast cancer is higher in their locality than in a neighboring rural area. (PCB levels were found to be higher in the soil of the urban community). If you find that in the urban community 20 out of 200 adult women have breast cancer and that in the rural community 10 out of 150 adult women have it, could you conclude, at a significance level of 0.05, that breast cancer is more prevalent in the urban community?1. The parameter of interest is:2. The hypotheses for this test are:3. The calculated test statistic is:4. The critical region is:5. Draw the critical region (make decision):6. It can be concluded that: