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- A large pizza chain has conducted a study to determine if the types of preferred pizza are independent of the region of the country where it is sold. One hundred random samples are selected in each region of the country with the following results. Areas Thin not Spicy Thin spicy Thick Crust not Spicy Thick Crust Spicy Total Samples Northeast 30 10 40 20 100 Northwest 25 20 45 10 100 Southwest 25 25 25 25 100 Southwest 15 30 10 45 100 Totals 95 85 120 100 400 Set up hypotheses to test if these preferred types of pizza are independent of the region of the country in which they are sold. Perform the appropriate statistical test to obtain your results. Calculate the p value and fully explain your results.Suppose that a random sample of size 1 is to be taken from a finite population of size N. a. How many possible samples are there?b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration.c. What is the difference between taking a random sample of size 1 from a population and selecting a member at random from the population?In an experiment with the effect of different feeding on sheep fertility, two feed categories were examined, A and B. 192 rivers were given feed category A and 190 were given feed category B. The following number of monocotyledonous and dicotyledonous sheep were obtained in each category: Feed category A Feed category B Monocotyledonous 60 82 Dicotyledonous 132 108 Examine with an appropriate hypothesis test whether there is a difference in fertility by feed category.
- Suppose that in a study of 35 million HPV shots examined, the shots were followed in time by 14,000 serious ailments and 32 confirmed deaths. However, suppose in examining a randomly selected control group of 35 million non-vaccinated people of the same age at a particular time A, 0.0413% developed a serious ailment soon after time A, and 0.000089% died soon after time A. What does the comparison of two groups tell us? What are the percentages in the vaccinated group (serious ailments and confirmed deaths), and how to they compare to the nonvaccinated group? Hint: compute the percentages for serious ailments (14,000/35,000,000) and confirmed deaths (32/35,000,000) for the vaccinated group. Compare with the control group. Notice % above. (0,0413% and 0.000089%) Answer here. What can we conclude with high probability, if this comparison between vaccinated and non-vaccinated groups was done many times with the same basic results? Answer here. Can we absolutely rule out that the…In analyzing the consumption of cottage cheese by members of various occupational groups, the United Dairy Industry Association found that 326 of 837 professionals seldom or never ate cottage cheese, versus 220 of 489 white-collar workers and 522 of 1243 blue-collar workers (Sheet 53). Assuming independent samples, use the 0.03 level in testing the null hypothesis that the population proportions could be the same for the three occupational groups. Sheet 53 Group 1 Group 2 Group 3 Total seldom or never 326 220 522 1068 often 511 269 721 1501 Total 837 489 1243 2569 Select one: a) chi-square stat = 4.81, crit. value = 7.01, fail to reject H0, population proportions are not different b) p-value = 0.09, reject H0, population proportions are not different c) chi-square stat = 4.81, crit. value = 9.2, fail to reject H0, population proportions are not different d) p-value = 0.029, reject H0, population proportions differentThe number of contaminating particles on a silicon waferprior to a certain rinsing process was determined for eachwafer in a sample of size 100, resulting in the followingfrequencies:Number of particles 0 1 2 3 4 5 6 7Frequency 1 2 3 12 11 15 18 10Number of particles 8 9 10 11 12 13 14Frequency 12 4 5 3 1 2 1a. What proportion of the sampled wafers had at leastone particle? At least five particles?b. What proportion of the sampled wafers had betweenfive and ten particles, inclusive? Strictly between fiveand ten particles?c. Draw a histogram using relative frequency on thevertical axis. How would you describe the shape of thehistogram?
- The following table shows the pesticide residue levels (ppb) in blood samplesfrom three groups of human subjects, A, B and C. Use the Kruskal-Wallis totest the null hypothesis, if there is no difference among the groups withrespect to the average level of pesticide residue at 5% significance level.If there is a significant difference, you are required to do a multiplecomparison test.A 10 26 11 30 9 44 12 15 42 23B 3 34 32 20 19 11 6 32 16 8C 14 5 10 11 5 9 11 9 13 14Determine if assumptions have been violated and if a between-subjects, one-way ANOVA can be completed: A biomedical engineer compared the abrasion resistance — as measured by number of rotations until failure — of three different artificial hips. Manufacturer X makes hip joints out of metal, manufacturer Y out of ceramic, and manufacturer Z out of a metal/ceramic composite. The biomedical engineer gets a random sample of 6 hips from each manufacturer’s production line and tests each one individually until failure occurs.a random sample of 60 and in terms of age groups was stratified as follows: 35 are youth (below 35yrs) ,15 are medium aged adults between 35-65yrs and 10 are elderly (above 65yrs).Your research outcome is to determine their attitude regarding compulsory putting on of masks wherever in public during lifting up of COVID -19 Lockdown. You carry out a survey to determine the above outcome and come up with the following observations. Those with positive attitude are 34 detailed as follows: Youth 20, medium adults 9 and elderly 5. Those with negative attitude were stratified as follows:15 youth,6 medium adults and 5 elderly. (i) Sketch a 3 by 2 contingency summary of this data (ii) State the hypothesis of this data, giving your α-level and degree of freedom Critical t-value from the chi-square distribution is 5.991
- a random sample of 60 and in terms of age groups was stratified as follows: 35 are youth (below 35yrs) ,15 are medium aged adults between 35-65yrs and 10 are elderly (above 65yrs).Your research outcome is to determine their attitude regarding compulsory putting on of masks wherever in public during lifting up of COVID -19 Lockdown. You carry out a survey to determine the above outcome and come up with the following observations. Those with positive attitude are 34 detailed as follows: Youth 20, medium adults 9 and elderly 5. Those with negative attitude were stratified as follows:15 youth,6 medium adults and 5 elderly. (i) Sketch a 3 by 2 contingency summary of this data (ii) State the hypothesis of this data, giving your α-level and degree of freedomConsider the large-sample level .01 test in Section 8.4 for testing H0: p=.2 against Ha: p>.2. a) For the alternative value p=.21, compute beta(.21) for sample sizes n=100,2500,10,000,40,000,and 90,000. b) For p^=x/n=.21, compute the P-value when n=100, 2500, 10,000, and 40,000. c) In most situations, would it be reasonable to use a level .01 test in conjunction with a sample size of 40,000? Why or why not?A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.8 3.9 5.0 3.4 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.5 4.2 4.6 5.0 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Note: If a two-sample t-test is appropriate, for degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.Use a calculator to calculate x1 , s1, x2 , and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (a) Do the data indicate that the violent crime rate in the Rocky Mountain…