Exp You are looking at a population and are interested in the proportion p that has a certain characteristic. Unknown to

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Exp You Are Looking At A Population And Are Interested In The Proportion P That Has A Certain Characteristic Unknown To 1 (36.43 KiB) Viewed 31 times

Exp You Are Looking At A Population And Are Interested In The Proportion P That Has A Certain Characteristic Unknown To 2 (36.43 KiB) Viewed 31 times

Exp You Are Looking At A Population And Are Interested In The Proportion P That Has A Certain Characteristic Unknown To 3 (35.28 KiB) Viewed 31 times

Exp You Are Looking At A Population And Are Interested In The Proportion P That Has A Certain Characteristic Unknown To 4 (36 KiB) Viewed 31 times

Exp You are looking at a population and are interested in the proportion p that has a certain characteristic. Unknown to you, this population proportion is p=0.65. You have taken a random sample of size n-105 from the population and found that the proportion of the sample that has the characteristic is p=0.67. Your sample is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "52", etc.) (a) Based on Sample 1, graph the 75% and 90% confidence intervals for the population proportion. Use 1.150 for the critical value for the 75% confidence interval, and use 1.645 for the critical value for the 90% confidence interval. (If necessary, consult a list of formulas) • Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with two decimal places . For the points (and), enter the population proportion, 0.65. 75% confidence interval 90% confidence interval E 0.49 0.82 0.49 0.32 065 0.65 ****** 0.49 0.82 0.49 0.82 (b) Press the "Generate Samples" button below to simulate taking 19 more samples of size -105 from the same population. Notice that the confidence intervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table. 75% 75% 90% 90% lower upper lower upper limit limit limit limit 7 75% confidence intervals 00% confidence intervals 51 0.67 ? ? 7 0.58 0.74 52 066 061 031
limit limit limit $1 0.67 7 7 ? 7 $2 0.66 0.61 0.71 0.58 0.74 S3 0.64 0.59 0.69 0.56 0.72 54 0.58 0.52 0.64 0.50 0.66 55 0.66 0.61 0.71 0.58 0.74 S6 0.64 0.59 0.69 0.56 0.72 $7 0.66 0.61 0.71 0.58 0.74 S8 0.58 0.52 0.64 0.50 0.66 S9 0.66 0.61 0.71 0.58 0.74 $10 0.58 0.64 0.50 0.66 0.52 $11 0.64 0.59 0.69 0.56 0.72 S12 0.66 0.61 0.71 0.58 0.74 $13 0.63 0.58 0.68 0.55 0,71 $14 0.71 0.66 $15 0.65 0.60 516 0.64 0.59 S17 0.74 0.69 0.76 0.64 0.78 0.70 0.57 0.73 0,69 0.56 0.72 0.79 0.67 0.81 S18 0.74 0.69 0.79 0.67 0.81 $19 0.64 0.59 0.69 0.56 0.72 520 0.64 0.59 0.69 0.56 0,72 > 6 limit E 0.49 75% confidence intervals 0.82 0.49 90% confidence intervals 0.82
0.49 0.82 0.49 0.82 18 (c) Notice that for -90% of the samples, the 90% confidence interval contains the population proportion. Choose the 20 correct statement. When constructing 90% confidence intervals for 20 samples of the same size from the population, exactly 90% of the samples will contain the population proportion. When constructing 90% confidence intervals for 20 samples of the same size from the population, at most 90% of the samples will contain the population proportion. When constructing 90% confidence intervals for 20 samples of the same size from the population, it is possible that more or fewer than 90% of the samples will contain the population proportion, (d) Choose ALL that are true. The 75% confidence interval for Sample 7 is narrower than the 90% confidence interval for Sample 7. This must be the case; when constructing a confidence interval for a sample, the greater the level of confidence, the wider the confidence interval. To guarantee that a confidence interval will contain the population proportion, the level of confidence must match the population proportion. For example, if p equals 0.48, then a 48% confidence interval will contain the population proportion. From the 90% confidence interval for Sample 7, we know that there is a 90% probability that the population proportion is between 0.49 and 0.82. If there were a Sample 21 of size 180 with the same sample proportion as Sample 7, then the 90% confidence interval for Sample 21 would be narrower than the 90% confidence interval for Sample 7. None of the choices above are true. ?