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Mendocino College *

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Statistics

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Apr 3, 2024

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For problems 1 & 2, a survey of 1200 Californian residents yielded 409 people who were born in other countries. 1. Find the point estimate of the proportion of all California residents who were born in other countries, to the nearest tenth of a percent. 409/1200 = .341 34.1% ----------------------------------------------------------------------------------------------------------------------------------------------- 2. Find the 95% confidence interval for this proportion to the nearest tenth of a percent. Calculator: stat/tests/A:1-PropZInt x 409 / n 1200 / C-Level 95% -------> 31.4 < p < 36.8 ----------------------------------------------------------------------------------------------------------------------------------------------- For the problems 3 & 4, a random sample of 60 mature redwood trees yield a sample mean diameter of 135.6cm and a sample standard deviation of 22.7cm 3. Find the 90% confidence interval for the population mean diameter, to the nearest tenth. Calculator: stat/tests/8:TInterval x x 135.6 / Sx 22.7 / n 60 / C-Level .9 --------> 130.7 < μ < 140.5 ----------------------------------------------------------------------------------------------------------------------------------------------- 4. At the 90% confidence level, find the margin of error (also called the maximum error/E) of the estimate of this mean to the nearest tenth. E= 1.645 (22.7/ √ 60) formula: CL (standard deviation/ √ number) 4.8cm --------------------------------------------------------------------------------------------------------------------------------------------- 5. Suppose you wanted to estimate the proportion of Californians born in other countries within 3% , at the 99% level of confidence, and that you have no prior knowledge of the sample proportion. What is the minimum sample size you would have to use? .25(2.576/.03)² formula: .25 ( cl / E)² = 1844 --------------------------------------------------------------------------------------------------------------------------------------------- 6. Using the standard deviation from problems #3 &4, find the minimum sample size you would have to use to estimate the average diameter of mature redwood trees within 5cm ( E ) at the 95% confidence level. n = (1.960 x 22.7)² = 80 formula: n = (confidence level x standard deviation / E )² “within” = E ---------------------------------------------------------------------------------------------------------------------------------------------- 7. To the nearest hundredth, what is the point estimate for the population mean of heights of female college students, if a random sample of seven female college students is selected and their heights are 162.5cm, 158.3cm, 182.1cm, 173.2cm, 160.9cm, 154.5cm and 151.3cm? “point estimate” is also x x ----> formula: input the heights into a List and then run 1-var stats to find the x x ----------------------------------------------------------------------------------------------------------------------------------------------- 8. You're testing the claim that the average guinea pig weighs 1.21 kg. A sample of 23 guinea pigs has an average weight of 1.04 kg, with a standard deviation of 0.51 kg. The test has a p-value of 0.124. Make a diagram showing the distribution, the parameter and the statistic. Shade and label the p-value. Notes: “the average guinea pig weighs...” means an evenly distribution on graph of the p-value μ 1.21 / x x 1.04 / Sx 0.51 / n 23 ----------------------------------------------------------------------------------------------------------------------------------------------- 9. You're testing the claim that at least 54% of Californians are bilingual. In a sample of 300 randomly selected Californians, 147 were bilingual. The test has a p-value of 0.041. make a diagram showing the distribution, the parameter and the statistic. Shade and label the p-value. Calculator: stat/tests/5: 1-PropZTest po .54 / x 147 / n 300 / <

10. What would the null hypothesis (Ho) be when testing the claim that the average miles per gallon of hybrid cars is under 50 miles per gallon? μ ≥ 50 mpg --------------------------------------------------------------------------------------------------------------------------------------------- 11. What would be the null hypothesis (Ho) be when testing the claim that a majority of people watch the TV news? P ≤ .50% -------------------------------------------------------------------------------------------------------------------------------------------- 12. What wold be the alternative hypothesis (H1) be when testing the claim that the standard deviation of scores on a standardized test is 25 points? (Standard deviation) σ ≠ 25points ------------------------------------------------------------------------------------------------------------------------------------------------ 13. To the nearest thousandth, what is the p-value for a test of the claim that the average microwave costs at most $125, if a random sample of 40 microwaves yielded a mean cost of $137, with a standard deviation of $26? Calculator: stat/tests/2: T-Test µo 125 / x x 137 / Sx 26 / n 40 / µ > (whatever the H1 symbol) = 0.003 ------------------------------------------------------------------------------------------------------------------------------------------------ 14. To the nearest thousandth, what is the p-value for a test of the claim that the average child says his or her first word before the age of 15 months, if a random sample of 35 children shows that the average age when they said their first word was 13.5 months and the sample standard deviation is 3.7 months? Calculator: stat/tests/2: T-Test µo 15 / x x 13.5 / Sx 3.7 / n 35 / µ < ( whatever the H1 symbol is) = 0.011 ------------------------------------------------------------------------------------------------------------------------------------------------ 15. To the nearest thousandth, what is the p-value for a test of the claim that at least 3/5 of community college students receive some sort of financial aid, if a randomly selected sample of 1400 college students yielded 822 who received financial aid? Calculator: stat/tests/5: 1-PropZTest po 3/5 / x x 822 / n 1400 / µ < ( whatever the H1 symbol is) = 0.163 ------------------------------------------------------------------------------------------------------------------------------------------------ 18. If the claim “A majority of American children own at least one videogame system” is tested at the 1% significance level, and the other test turns out to have a p-value of 0.027, what is the final conclusion? (summarize the results) Ho: p ≤ .5 H1: p > .5 (claim) (p-value) 0.027 > 0.01 (significance level) do not reject Ho Summary: There isn't sufficient evidence to support the claim that a majority of American children own at least 1 videogame system. ------------------------------------------------------------------------------------------------------------------------------------------------ 19. If the claim “The average cat weighs less than 3.2kg” is tested at the 5% significance level, at the p-value of the test turns out to be 0.042, what is the final conclusion? (summarize the results) Ho: p ≥ 3.2kg H1: p < 3.2kg (claim) (p-value) 0.042 < 0.05 (significance level) reject Ho Summary: There is sufficient evidence to support the claim that the average cat weighs less than 3.2kg ------------------------------------------------------------------------------------------------------------------------------------------------ is (reject Ho) reject (Ho claim) There sufficient evidence to the claim that ... is not (do not reject Ho) support (Hi claim) ------------------------------------------------------------------------------------------------------------------------------------------------ Calculator: to find data from a List: stat/calc/1:1VarStat C-level 99% 2.576 95% 1.960 < less than, below, fewer than, up to, faster than the average 90% 1.645 > greater than, exceeds, in excess of, older, taller ≤ at most, no better than ≥ at least, not less than = hasn't changed from, is the same as ≠ is different from, has changed from, is not the same as The majority p > .5 The minority p < .5

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