Is the difference between the two indicators significant at the 95% confidence level?
Q: What is the purpose of the confidence intervals in Statistics?
A: Confidence interval is derived from the Sample stastics for the estimatation of population…
Q: what is measured by a confidence interval and describe the factors that affect the width of a…
A: How much ambiguity there is for any given statistic is a confidence interval. Confidence intervals…
Q: Why does increasing the confidence level result in a larger margin of error?
A: We know that the Margin of error is directly proportional to the test statistic's critical value,…
Q: Use these data to calculate the 95% confidence interval for the relative risk
A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: The confidence interval was (41%, 45%) What was the margin of error? +/- % What was the summary…
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Q: Why does a decrease in sample size generally yield larger confidence intervals?
A: Confidence interval is the interval estimate of an unknown population parameter. It gives the…
Q: What is the one exception to using the z score for confidence intervals?
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Q: What does a 95% confidence level mean?
A: The 95% confidence level means that if the hypothesis test is repeated on the certain process, then…
Q: Given certain level of significance, what is the relationship between the confidence interval and…
A: We want to know that relationship between confidence interval sand sample size.
Q: Suppose you had a sample size of 41 and the population distribution was normal. Which approach would…
A: Here we use basic criteria for getting best interval estimation of mean
Q: Explain the Other Types of Confidence Intervals.
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Q: What proportion of your confidence intervals include the true population mean? Is this proportion…
A: Consider a confidence interval of 95%. That is, the proportion that the confidence interval will…
Q: If you think a data point is an outlier, what test can you perform to see if you should omit the…
A: Given that the number of data points in the set is 8.
Q: What should your sample size be if you want a confidence level of 90 percent and a margin of error…
A: We want to find the sample size (n)
Q: Explain the type of Equation used for confidence interval calculation?
A: A confidence interval gives an approximate range of values which is likely to include an unknown…
Q: If a researcher uses 90% confidence level, what is the level of significance?
A: We have given that, Confidence level (C.I) = 90% = 0.90 Then, We will find the level of…
Q: What does Level of Confidence indicates?
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Q: Explain the steps in computing a confidence interval for ρ?
A: Introduction: The steps to construct a confidence interval in general are: Identify a sample…
Q: What is the effect of increasing the confidence level on the margin of error?
A: The formula for calculating the margin of error is, The margin of error is directly proportional…
Q: What is the relationship between α and the confidence level of a hypothesis test?
A: In hypothesis testing, α is the level of significance, which provides details about the chance of…
Q: Explain when you would use the z value or the t-value to calculate a confidence interval
A: Z value: The z value is used for finding the confidence intervals for single population proportion,…
Q: What is the relationship between variation in a data set and the width of the confidence intervals…
A: Confidence intervals tell you the most likely range of the unknown population average or percentage…
Q: What is the 90% confidence interval of the mean?
A: A confidence interval is an interval that has the property that is very likely that the population…
Q: What are two ways to get a narrower confidence interval for a proportion?
A: Two ways to get a narrower confidence interval for a proportion are:
Q: Why is a 99% confidence interval wider than a 95% confidence interval?
A: The confidence interval formula is sample statistic±Margin of error. The margin of error is the…
Q: What is z* for a 92% confidence level?
A: To find value of Z* for a 92% confidence level ??
Q: What effect does increasing the sample size have on the width of a confidence interval? I know that…
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Q: onstruct a 95 confidence interval for p.
A: Here use confidence interval for proportion
Q: What is the difference between a prediction interval and a confidence interval? And when is it…
A: Confidence Interval : Confidence intervals tell you how well you have determined a parameter of…
Q: if you increase the sample size and confidence level at the same time. what will happen to the width…
A: The formula for the confidence interval (say) for population mean is : C.I= x ± zα/2.s2n As the…
Q: Define relationship between confidence intervals and significance tests?
A: Test: Denote τ as a population parameter of interest. Suppose sample data are collected from the…
Q: Suppose we would like to estimate the proportion of all NBA fans who thought Aaron Gordon won the…
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Q: Explain the Interpretation of confidence level.
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Q: Explain the three properties of confidence intervals.
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Q: What is the difference between the different confidence interval formulas?
A: Confidence interval is the estimate of the interval of an unknown population parameter. It provides…
Q: What is the effect on a confidence interval if one decreases both sample size and the level of…
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Q: A quality control specialist wants to estimate the percentage of defective batteries within 5% from…
A: A quality control specialist wants to estimate the percentage of defective within 5% from the true,…
Q: What is a confidence interval in statistics?
A: In inferential statistics, the two types of estimation are: point estimate and confidence interval…
Q: Why are confidence intervals important and what do they mean to a study?
A: The confidence interval at 100 (1 – α) % confidence level gives us an interval estimate about the…
Q: Michelle, a student studying music, randomly sampled fellow music majors and asked whether they…
A: Given information- Confidence interval = (0.09, 0.26) We have to find margin of error. We know that-…
Q: What is the relationship between confidence intervals and hypothesis tests?
A: Confidence Interval:Confidence interval is the interval estimate of the population parameter. It is…
Q: What is meant by saying that a 1−α confidence interval is a. exact? b. approximately correct?
A: a) 1−α confidence interval is Exact means that the probability that the unknown value of population…
Q: What is the formula for the mean absolute deviation formula for paired data sets?
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Q: How can you make a 95% confidence interval smaller without changing the confidence level?
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Q: What two conditions will result in the use of the student-t distribution when constructing a…
A: Confidence interval for mean: When the sample size is large (n>30) and population variance (or…
Q: What happens to the interval width as confidence level increases? Why?
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Q: Aston’s Career Service wants to find out what proportion of Aston’s students work in a part-time…
A: From the given information, Population proportion = p = 60% = 0.60 Margin of error = E = 4% = 0.04…
Q: explain the logic behind why confidence intervals with higher confidence levels are wider than…
A: Confidence interval: A confidence interval is a way to measure the degree of uncertainty (or…
Q: It states that there is significant difference between the observed and expected data.
A: Alternative Hypothesis
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- Independent random samples of patients who had received knee and hip replacement were asked to assess the quality of service on a scale from 1 (low) to 7 (high). For a sample of 83 knee patients, the mean rating was 6.543 and the sample standard deviation was 0.649. For a sample of 54 hip patients, the mean rating was 6.733 and the sample standard deviation was 0.425. Test, against a two-sided alternative, the null hypothesis that the population mean ratings for these two types of patients are the same.In a study of morphological variation in natural populations of fruit fly, it was reported that the mean wing length of 16 females, collected in a certain area, was 4.653 mm with s = 0.012 mm; and the mean wing length of 11 females, collected in a second area, was 4.274 mm with s = 0.02. Let the distribution of the wing length be normal, find a 98% confidence interval on the ratio of the two populations’ standard deviations.1 Suppose that the average time spent per day with digital media several years ago was 3 hours and 22 minutes. For last year, a random sample of 20 adults in a certain region spent the numbers of hours per day with digital media given in the accompanying table. Preliminary data analyses indicate that the t-interval procedure can reasonably be applied. Find and interpret a 90% confidence interval for last year's mean time spent per day with digital media by adults of the region. (Note: x=5.88hr and s=2.27hr.) The 90% confidence interval is from ( ? ) hour(s) to ( ? )hour(s). Interpret the 90% confidence interval. Select all that apply. A. There is a 90% chance that the mean amount of time spent per day on digital media last year by all adults in the region is between the interval's bounds. B.With 90% confidence, the mean amount of time spent per day on digital media last year by all adults in the region is between the interval's bounds. C.90% of all…
- A large school district found that 88 of 100 randomly selected students at East High School had internet access at home . A separate random sample from West High showed 79 of 100 students had internet access at home Administrators used those results to make a 90\% confidence interval to estimate the difference between the proportion of students at each school who have internet access at home (p Z -p W ) . resulting Interval was approximately 0.09 plus/minus 0.086 . They want to this interval to test H 0 * p 0 =p w versus H k :p k ne pw at the alpha = 0.10sisnl significance levelAssume that all conditions for Inferance been mel Based on the Intervalwhat do we know about the corresponding P-value and condusion at the alpha = 0.10 level of significance?. A taxi company has been using Brand A tires, and the distribution of kilometers to wear-out has been found to be approximately normal with mean =114,000 and σ = 11,600. Now it tries 12 tires of Brand B and finds a sample mean 117,200. Test at the 5% level of significance to see whether there is a significant difference (positive or negative) in kilometers to wear-out between Brand A and Brand B. In the problem above, if the true kilometers to wear-out is 114,000, what is the 95% confidence interval for sample means? First show how to get the critical z values.The tensile strengths of two types of materials were investigated by collecting 16 samples of each material (totally 32 samples).The sample mean for material 1 was 423.08 (psi), and for material 2 was 424.7 (psi). The samplestandard deviation of the difference in tensile strengths was sD = 2.8 (psi). Is there sufficientevidence to conclude that two types of materials have the same tensile strength? Formulate andtest the appropriate null H0 and alternative hypotheses H1 to verify the claim at level α = 0.01
- The mean ± 1 SD of calcium intake (in mg) among 25 females, 12-14 years of age, below the poverty level is 6.56 ± 0.64. Similarly, the mean ± 1 SD of calcium intake among 40 females, 12-14 years of age, above the poverty level is 6.80 ± 0.76. Do we have sufficient evidence to conclude that the mean intake of calcium among females below the poverty level is significantly lower than the calcium intake of females above the poverty level? State the null and alternative hypothesis in mathematical notation Ho: Ha: What is the level of significance to be used? What is the appropriate test statistic? Why? What is the critical region? Compute for the test statistic. Show all your computations below. What is the statistical decision? What is your basis for such decision? How would you conclude your findings? Be specific.Is the proportion of wildfires caused by humans in the south different from the proportion of wildfires caused by humans in the west? 394 of the 533 randomly selected wildfires looked at in the south were caused by humans while 388 of the 554 randomly selected wildfires looked at the west were caused by humans. What can be concluded at the = 0.01 level of significance? For this study, we should use Select an answer z-test for the difference between two population proportions t-test for the difference between two dependent population means z-test for a population proportion t-test for the difference between two independent population means t-test for a population mean The null and alternative hypotheses would be: Select an answer p1 μ1 Select an answer > ≠ < = Select an answer μ2 p2 (please enter a decimal) Select an answer p1 μ1 Select an answer > = < ≠ Select an answer p2 μ2 (Please enter a decimal) The test statistic ? z t = (please show your…Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield (bar x) x=99.3, (bar y) y=99.5, r=0.943, P-value=0.000, and (^ over y) y=−5.29+1.06x, where x represents the IQ score of the younger child. Find the best-predicted value of (^ over y) y given that the younger child has an IQ of108?Use a significance level of 0.05. The critical values of the Pearson correlation coefficient r. Critical Values of the Pearson Correlation Coefficient r n α=0.05 α=0.01 NOTE: To test H0: ρ=0 against H1: ρ≠0, reject H0 if the absolute value of r is greater than the critical value in the table. 4 0.950 0.990 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.590…