With larger and larger numbers of categories in chi-square tests, the chi-square distribution takes on the shape of the _______ distribution. Poisson binomial t– normal
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With larger and larger numbers of categories in chi-square tests, the chi-square distribution takes on the shape of the _______ distribution.
- Poisson
- binomial
- t–
- normal
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- A sales manager for a large department store believes that customer spending per visit with a sale is higher than customer spending without a sale, and would like to test that claim. A simple random sample of customer spending is taken from without a sale and with a sale. The results are shown below. Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Confidence Level Without sale with sale 74.894 78.138 1951.47 1852.0102 200 0 419 0.813 0.208 1.648 0.417 1.966 95% 300 Samples from without sale: nwithout Samples from with sale: nwith Point estimate for spending without sale: Twithout Point estimate for spending with sale: with - = Ex: 9 - - -3 -2 Ex: 1.234 P t -1 || = 0 Ex: 1.234 1 2 3A hospital wants to determine if the type of treatment for pneumonia is a factor in recovery time? The table below shows the number of days to recovery for several randomly selected pneumonia patients that had various types of treatment. Sent Home With Medicine A Few Hours in the Hospital Overnight Hospital Stay 26 25 17 14 25 17 13 25 24 22 7 24 4 21 11 14 19 16 20 12 19 21 21 Assume that all distributions are normal, the three population standard deviations are all the same, and the data was collected independently and randomly. Use a level of significance of a = 0.05. Ho: µi = µ2 = µ3 H1: At least two of the means differ from each other. 1. For this study, we should use Select an answer e (Please show your answer to 3 decimal places.) 2. The test-statistic for this data = (Please show your answer to 4 decimal places.) 3. The p-value for this sample = a 4. The p-value is Select an answer O hypothesis 5. Base on this, we should Select an answer 6. As such, the final conclusion is…Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 35 and p = 0.28. (For each answer, enter a number. Use 2 decimal places.)n·p = n·q = Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂ _____ be approximated by a normal random variable because _____ _____.
- 1.42 Solver and least squares fits 1.43 Error and statistics The objectives of this section are to: 1. Create error bars within a chart in a spreadsheet. 2. Apply statistics-related functions for a data series. 3. Calculate and distinguish between standard deviation and quartiles for a data series. 4. Complete a linear regression within a spreadsheet using functions or built-in regression tools. Error and error bars An error is commonly known as a mistake, but in a spreadsheet, an error usually quantifies a statistical difference. Ex: A residual is the difference between the data and model, which is detailed in another section, and is one example of a quantifiable error. When plotting data and models in charts, error bars provide one method to visualize quantified error. The animation below shows several types of error bars. PARTICIPATION ACTIVITY 1.43.1: Types of error bars. Start 2x speed 100 y-axis error bar Property 80 with cap Error value y-axis 60- error bar without cap x and y…Regression. A coach wants to see the relationship between the statistics of practice games and official games of a local soccer team. A sample of 24 players was used and the resulting (partial) Excel output is shown below. Assume both x and y form normal distributions. Regression Statistics Multiple R *** R Square 0.70524 Adjusted R Square 0.668395 Standard Error 8.703633 Observations 24 Coefficients Standard t Stat P-value Lower Upper 95% Error 95% Intercept 40.63461 8.506861 4.794266 0.001366 21.1673 60.40101 Midterm 0.718205 0.174917 4.379587 0.002365 0.362046 1.16907840% Question* Consider that the mumber of flaws occurring in each 100 feet of material follows the Poisson distribution with an average of 2 flaws. The probability that in 250 feet of material will occur at least4 feet is: None of these 0.8753 0.7350 0.5595 Question
- A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey of adults found that 46% have used a multivitamin in the past 12 months You randomly select 50 adults and ask them past 12 months. they have used a multivitamin in the Select the correct answer below and, if necessary, fill in the answer boxes within your choice O A. No, because np <5. OB. No, because ng <5. O C. Yes, the mean is and the standard deviation is (Round to two decimal places as needed.)K A poll of 2,082 randomly selected adults showed that 86% of them own cell phones. The technology display below results from a test of the claim that 94% of adults own cell phones. Use the normal distribution as an approximation to the binomial distribution, and assume a 0.01 significance level to complete parts (a) through (e). Test of p=0.94 vs p *0.94 Sample X N 2,082 1 1800 Sample p 0.864553 95% CI (0.845236,0.883871) a. Is the test two-tailed, left-tailed, or right-tailed? OTwo-tailed test O Right tailed test O Left-tailed test b. What is the test statistic? The test statistic is. (Round to two decimal places as needed.) c. What is the P-value? The P-value is (Round to three decimal places as needed.) d. What is the null hypothesis and what do you conclude about it? Z-Value - 14.50 P-Value 0.000 EXEDq10
- Based on this graph what is the approximate distribution of data? X~___(___,___)Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 40 and p = 0.18. (For each answer, enter a number. Use 2 decimal places.)n·p = n·q = Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____, p̂ _____ be approximated by a normal random variable because _____ _____.first blank YesNo second blank cancannot third blank n·q does not exceedboth n·p and n·q exceed n·p and n·q do not exceedn·p exceedsn·p does not exceedn·q exceeds fourth blank (Enter an exact number.)What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.)μp̂ = mu sub p hat = σp̂ = sigma sub p hat = (b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)_____,…Which of the following is true about the homogeneity of variances assumption? You need to obtain a new set of data You must calculate Cohen's d If unequal, you should exclude some participant data It cannot be violated if you want to conduct an independent samples t-test