Q.5.1 What is a sampling distribution? Q.5.2 Explain the term "standard error" in relation to a distribution of sample means. Q.5.3 Give a brief explanation of the central limit theorem.
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- 1. Student's t test for correlated groups really reduces to _________. a. the sign test b. Student's t test for single samples using difference scores c. Students t test for independent groups d. none of the above 2. The z test for independent groups is seldom used because _________. it lacks sensitivity it is too complicated we seldom know the population variances the sampling distribution of z under H0 is unknown 3. In a t test, when the size of the sample is increased, the confidence interval _________. increases decreases stays the same changes shape a and d 4. As the df increases, the t distribution _________. gets more symmetrical approaches the normal distribution stays the same becomes more skewed10 2llustration 9.4. The first and third columns of Table 9.3 give the frequency distribution of the average monthly earnings of male workers. Calculate the mean earnings. TABLE 9.3. DISTRIBUTION OF MALE WORKERS BY AVERAGE MONIHLY EXPENSES (Computation of Arithmetic Mean . . . Long Method) Monthly earnings Mid-point No. of workers Rs Rs Rs m fm 3,600 5,320 6,800 9,630 20,500 23,595 34,080 42,250 27.5 - 32.5 30 120 32.5–37.5 35 152 37.5–42.5 40 170 42.5 47.5 45 214 47.5 – 52.5 50 410 52.5 57.5 55 429 57.5 62.5 60 568. 62.5-67.5 65 650 55,650 68,625 59,600 45,050 23,310 14,440 10,700 5,250 2,750 67.5 -72.5 70 795 72.5 -77.5 77.5-82.5 75 915 80 745 82.5-87.5 85 530 87.5-92.5 90 259 92.5-97.5 95 152 97.5 - 102.5 100 107 102.5--107.5 105 SO 107.5 -112.5 110 25 Σ 6,291 4, 31,1 50
- A variable of a population has a mean of u 200 and a standard deviation of o = 42. a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean b. For part (a) to be true, what assumption did you make about the distribution of the variable under consideration? A. No assumption was made. B. Normal distribution. C. Uniform distribution. c. Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not? A. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true. O B. Yes, the sampling distribution of the sample mean is always normal. and standard deviation C. No, the sampling distribution of the sample mean is never normal for sample size less than 30.17-7
- Dr. Smith conducts research concerning the association between deception and trust of other individuals. She recruits six subjects to take part in their study. Each subject is also asked to "list the number of times you have lied in the past week," as a measure of deception. Also, each subject is asked, "on a scale of 1 to 7 (1 being none and 7 being a lot) how much do you trust individuals?" Here is the data: Ps Deception (X) 1 2 13 st 15 16 |4 3 7 2 5 H₁: | 13 The research hypothesis is that there is an association between deception and trust of people. ♦ Step 1. Express the substantive question as two statistical hypotheses. Ho: ◄► Trust (Y) 14 14 13 ♦ (O ◆ 6 13 14A variable of a population has a mean of μ=100 and a standard deviation of σ=42 a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean ____ and standard deviation ____ b. For part (a) to be true, what assumption did you make about the distribution of the variable under consideration?A. Normal distribution.B. No assumption was made.C. Uniform distribution. c. Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not?A. No, the sampling distribution of the sample mean is never normal for sample size less than 30.B. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.C. Yes, the sampling distribution of the sample mean is always normal.12.1.11-T Question Help ▼ A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the a= 0.05 level of significance. H Click the icon to view the table. H: The distribution of colors is the same as stated by the manufacturer. C. None of these. Compute the expected counts for each color. Color Frequency Expected Count Brown 59 Yellow 64 Red 57 Blue 61 Orange 88 Green 66 (Round to two decimal places as needed.) Enter your answer in the edit fields and then click Check Answer. parts remaining Clear All Check Answer W MAY 4 F11 F12 F9 F10 F8 ロロ口 DOO F4 F7 F6 吕口 F5 F3 esc F2 F1 & delete $ 7 8 9. 4 5 2 P Y U E R Q J K F G D. #3