Assume that for a e R, f is 21.–periodic, g (z) = f (-r) and h (z) = f ( – a). Denote by Af and Bị the Fourier coefficients of f. For all n > 1, show that (Explain clearly all the steps!): (a) Af = B3, Ag = Ag, and B{ = – B;. (b) Af = Aß, A; = Af cos - B{ sin # and B = Af sin # + B, cos ".
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- It has been noted that the amount of time people spend shopping in supermarkets incountry X has decreased due to the discovery of a new strain of Covid19. Based onthis realization,the manager of Power Supermarket decided to collect data for thelength of time people spend in his supermarket during a one week period. He is aimingto use the data to help him decide if the supermarket should be converted to a virtualsupermarket/a delivery based one.a. Use the information below to construct two frequency polygons.b. Do you think that Power Supermarket should close their doors?Explain your answer.*Assume that a person who spends more time in a supermarket buys a lot of goods anda person who spends a short time in a supermarket,buys few goods Beforethepandemic: Time Frequency1-5 506-10 2511-15 2216-20 8021-25 6026-30 4531-35 3 After the pandemic:Time Frequency1-5…The spike stature of the plants grown from the seeds of the porcine separates (Dactylis glomerata L) collected from the University campus and İbradı Eynif pasture are given below. In this plant, compare whether there is a difference between regions in terms of spike height. Virgo Height (cm) Data obtained from plants collected from university campus 5 6 8 7 8 6 5 5 4 6 6 Data obtained from plants collected from Eynif pasture 12 9 11 9 9 11 9 10 11 10 Note: Your results interpretation according to two different possibilities (Do it separately, assuming that it is 0.07 and 0.04).Julia is a boutique shop owner in her town. Due to covid-19 pandemic, wearing a facemask of a person is required for their safety. Since there are limited stocks available, she decided to start another business by making a facemask. She started selling facemask from day 1 to day 10. The data she collected is shown in the table below
- A research center claims that at least 28% of adults in a certain country think that their taxes will be audited. In a random sample of1000 adults in that country in a recent year, 23%say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. nothing% of adults in the country think that their taxes will be audited. B. Less than nothing% of adults in the country think that their taxes will be audited. C. At least nothing% of adults in the country think that their taxes will be audited. D. The percentage of adults in the country who think that their taxes will be audited is not nothing%. Let p be the population proportion of…. A research center claims that at least 23% of adults in a certain country think that their taxes will be audited. In a random sample of 900 adults in that country in a recent year, 19% say they are concerned that their taxes will be audited. At α=0.01, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha.A research center claims that at least 31% of adults in a certain country think that their taxes will be audited. In a random sample of 800 adults in that country in a recent year, 26% say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. The percentage of adults in the country who think that their taxes will be audited is not enter your response here%. B. enter your response here% of adults in the country think that their taxes will be audited. C. Less than enter your response here% of adults in the country think that their taxes will be audited. D. At least enter your response here% of adults in the country think…
- A research center claims that at least 31% of adults in a certain country think that their taxes will be audited. In a random sample of 800 adults in that country in a recent year, 28% say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. ______% of adults in the country think that their taxes will be audited. B. The percentage of adults in the country who think that their taxes will be audited is not ______%. C. Less than ______% of adults in the country think that their taxes will be audited. D. At least ______% of adults in the country think that their taxes will be audited. (b) Find the critical value(s) and identify the rejection region(s). (c)…6. A research center claims that at least 30% of adults in a certain country think that their taxes will be audited. In a random sample of 1200 adults in that country in a recent year, 26% say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. Question content area bottom Part 1 (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. enter your response here % of adults in the country think that their taxes will be audited. B. The percentage of adults in the country who think that their taxes will be audited is not enter your response here %. C. At least 30 30% of adults in the country think that their taxes will be audited. Your answer is correct. D. Less than…Produce a CROSSTAB for the variables CLASS and RECYCLE. Before conducting your analysis, first reverse code SATJOB so that 1 = Very Dissatisfied; 2=Moderately Dissatisfied; 3=Moderately Satisfied; and 4=Very satisfied. Set all other values (8, 9) to system missing. Then examine the relationship between social class and job satisfaction by testing both statistical significance and strength of association. Use chi-square for significance and choose the appropriate measures for strength of association (Phi, Cramer’s V, Lambda, or Gamma). Set alpha to .05. State the null and research hypotheses: H0: H1: What is the obtained chi-square value? What is the significance level (p-value) for the obtained chi-square? Should we reject or fail to reject the null hypothesis? Is there a statistically significant relationship between these variables? Which measure of association would be most appropriate for these variables? What is the value of the measure of association? Interpret your findings by…
- Check whether the data in this problem satisfy the Hawkins–Simoncondition.An industry trade publication stated that the average profit per customer for this industry was at least $4500. Using a test of hypothesis, do the data support this claim or not Customer Percent Gross Profit Gross Sales Gross Profit Industry Code Competitive Rating* 1 51.0% $170.00 $86.70 1 2 2 32.0% $181.00 $57.92 3 4 3 20.0% $203.00 $40.60 2 2 4 22.0% $249.00 $54.78 5 1 5 21.0% $476.00 $99.96 5 1 6 21.0% $476.00 $99.96 5 4 7 22.0% $635.00 $139.70 2 3 8 34.0% $856.00 $291.04 3 3 9 26.0% $1,062.00 $276.12 4 2 10 16.6% $1,110.00 $183.71 7 3 11 20.0% $1,153.00 $230.60 7 3 12 36.0% $1,392.00 $501.12 4 2 13 18.0% $1,743.00 $313.74 4 2 14 20.0% $2,307.00 $461.40 7 3 15 5.0% $2,534.00 $126.70 4 5 16 29.0% $2,683.00 $778.07 7 2 17 10.0% $2,780.00 $278.00 2 3 18 37.0% $3,272.00 $1,210.64 5 3 19 60.0% $3,864.00 $2,318.40 7 1 20 24.0% $3,988.00 $957.12 6 3 21 9.0% $4,072.00 $366.48 7 3 22 50.0% $4,190.00 $2,095.00 5 3 23 17.0% $4,219.00 $717.23 3…A panel of dentists is interested in testing two different toothpaste brands (A and B) to see if there is a relationship between the brand and whether or not the patient has a cavity at their next appointment. A representative sample of 60 patients is recruited to take part in this study. At their first appointment of the year, each subject is assigned to brush their teeth with one of the two brands for the next six months. At their follow-up appointment six months later, they were checked for cavities. ******In the sample, 6 of the 30 patients assigned to Brand A were found to have a cavity. The fraction 6/30 should be denoted by which of the following? μ x̄ p p̂ n s σ χ²