You are conducting a multinomial hypothesis test for the claim that the 4 categories occur with the following frequencies: Category A B C D Observed Frequency 49 11 30 33 = Ho: PA = 0.4; PB = 0.1; PC What is the chi-square test-statistic for this data? 0.2; PD = 0.3
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- Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows: Age Number of Driver Deaths per 100,000 16–19 38 20–24 36 25–34 24 35–54 20 55–74 18 75+ 28 Use the 4 steps of hypothesis testing to see if the prediction is significant with a criteria of alpha=.05 on the following data For each age group, pick the midpoint of the interval for the X value. (For the 75+ group, use 80.)A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: 105.6 90.9 91.2 96.9 96.5 91.3 100.1 105.5 99.6 107.7 103.3 92.4 Does this data suggest that the population mean reading under these conditions differ from 100? State the null and alternative hypotheses. Calculate, correct to 2 decimal places, the sample mean, x ; and the sample standard deviation, s. Evaluate the appropriate test statistic. Test these hypotheses at 05 level of significance.A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: 104.3 89.6 89.9 95.6 95.2 90.0 98.8 103.7 98.3 106.4 102.0 91.1 a)Does this data suggest that the population mean reading under these conditions differs from 100? State and test the appropriate hypotheses using =.05. b) Suppose that prior to the experiment, a value of teta=7.5 had been assumed. How many determinations would then have been appropriate to obtain beta=.10 for the alternative u=95 ?
- The following data are on the dental measurements (distance in mm from the center of the pituitary to the pterygomaxillary fissure of 11 girls and 16 boys, all of whom were 16 years of age. a) What are the appropriate null and alternative hypotheses for this research question using the appropriate population parameter(s) for SAS output for a t-test? b) Based on the output, which p-value tests the following hypotheses if you want to use a two-sample independent pooled t-test? Provide the specific test statistic and p-value. c) From the output, what is the estimate of the pooled standard deviation? d) From the output, what is the standard error for the average difference in dental measurements in the population of 16-year-old boy and 16-year-old girls (assume the population variances are equal)?An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola. Beverage Sample Size Sample Mean Sample SD Strawberry Drink 10 535 24 Cola 10 559 15 Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use ? = 0.05.) State the relevant hypotheses. (Use ?1 for the strawberry drink and ?2 for the cola.) H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≥ 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0 H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. Reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.Reject H0. The…The NAEP considers that a national average of 283 is an acceptable performance. Using α = .05, run a two-tail t-test for one sample to test Ho: µ=283 for the 2019 scores. Report the t-obt, df, and p-values. Would you reject the null hypothesis that the 2019 scores come from a population with average 283? If this is the case, does it come from a population from larger or smaller average?
- The effectiveness of a new bug repellent is tested on 1616 subjects for a 10 hour period. (Assume normally distributed population.) Based on the number and location of the bug bites, the percentage of surface area exposed protected from bites was calculated for each of the subjects. The results were as follows: ?⎯⎯⎯=92x¯=92, ?=13 s=13 The new repellent is considered effective if it provides a percent repellency of at least 9090. Using ?=0.05α=0.05, construct a hypothesis test with null hypothesis ?≤90μ≤90 and alternative hypothesis ?>90μ>90 to determine whether the mean repellency of the new bug repellent is greater than 9090 by computing the following: (a) the degree of freedom (b) the test statistic The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that ?≤90μ≤90. Our results do not provide enough evidence that the new bug repellent is effective. B. We can reject the null hypothesis that ?≤90μ≤90. Our results indicate that…You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:HoHo : pA=0.4 pB=0.3 ; pC=0.15 ; pD=0.15Complete the table. Report all answers accurate to three decimal places. Category ObservedFrequency ExpectedFrequency Residual A 44 B 34 C 32 D 19 What is the chi-square test-statistic for this data?χ2=For significance level alpha 0.1, what is the chi-square Critical Value?Critical Value = What would be the conclusion of this hypothesis test? Reject the Null Hypothesis Fail to reject the Null Hypothesis Report all answers accurate to three decimal placesThe following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population mean μ.u<52 t=-4.479421 p=0.000020 x=51.87 Sx=0.21523 n=55Do you reject H0 at the a=0.10 level of significance? Question 5 options: No Yes
- In a hypothesis test with hypotheses H0 :pless than or greater than 0.58 and H1 >0.58 , a random sample of size 1,165 produced a sample proportion of 0.6160. The test is to be made at the 2.5% significance level. What is the value of the test statistic, z, rounded to three decimal places?The average annual miles driven per vehicle in the United States is 11.1 thousand miles, with σ ≈ 600 miles. Suppose that a random sample of 36 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.9 thousand miles. Does this indicate that the average miles driven per vehicle in Chicago is different from (higher or lower than) the national average? Use a 0.05 level of significance. State the null and alternate hypotheses. a) H0: p = 11.1; H1: p > 11.1 b) H0: p = 11.1; H1: p < 11.1 c) H0: μ = 11.1; H1: μ > 11.1 d) H0: μ = 11.1; H1: μ ≠ 11.1 e) H0: p = 11.1; H1: p ≠ 11.1 f) H0: μ = 11.1; H1: μ < 11.1 (b) What sampling distribution will you use? What assumptions are you making? a) The standard normal, since we assume that x has a normal distribution with known σ. b) The Student's t, since we assume that x has a normal distribution with unknown σ. c) The Student's t, since we assume that x has a normal distribution with known σ.…You are conducting a multinomial hypothesis test for the claim that the 4 categories occur with the following frequencies:HoHo : pA=0.3; pB=0.1; pC=0.4; pD=0.2 Category ObservedFrequency A 26 B 13 C 34 D 13 What is the chi-square test-statistic for this data?χ2=Report all answers accurate to three decimal places.
