Part 1 of 5 The table below shows the distribution of births across the days of the week in a random sample of 145 births from local records in a large city: Days Sun Mon Tue Wed Thu Fri Sat Births 19 16 26 26 16 24 18 Are births evenly distributed across the days of the week? Use 5% level of significance. Procedure: Goodness of Fit Test 3 V 0' Assumptions: (select everything that applies) At most 20% of the expected frequencies are less than 5 Independent samples Simple random sample Equal population standard deviations Normal populations .All expected frequencies are 1 or greater 0' \\/ Part 2 of 5 Step 1. Hypotheses Set-Up: H1]: the variable has the specified distribution 6 " 0' Ha: the variable doesn't have the specified distribution 3 " 0' , and the testis Right-Tail t V 0' Step 2. The significance level a = o' 96 Part 3 of 5 Step 3. Compute the value of the test statistic using the table below: (Round the answers to 4 decimal places) 2 Category [D]bserved [E]xpected O E (o _ 532 1%. Sun 19 C] -1.7143 2.9333 0.1419 Mon 13 20.7143 C] 22.2243 1.0729 Tue 23 20.7143 5.2357 C] 1.3433 Wed 23 20.7143 5.2357 27.9333 C] Thu 13 20.7143 4.7143 22.2243 1.0729 Fri 24 20.7143 3.2357 10.7953 0.5212 Sat 13 20.7143 -2.7143 7.3374 0.3557 2 Tm\" l:] = Z: W = C] d= C] Step 4. Testing Procedure: (Round the answers to 3 decimal places) CVA PVA Provide the critical value(s) for the Rejection Compute the P-value of the test Region: statistic: left CV is l:] and right CV is C] P-value is C] Question Help: EiVideo Q Written Example In the world population, 80.8% of all people have dark brown or black hair, 10.2% have brown hair, 6.2% have blond hair and 2.8% have red, gray, or white hair. A researcher wants to see if the distribution of hair color is different for the residents of Salt Lake City. The table below shows the results of a random sample of 983 residents in Salt Lake City. What can be concluded at the significant level of a = 0.01. Round answers to 4 decimal places, do not round between steps. Your friend Alicia helped you with the null and alternative hypotheses... H0: The distributions of hair colors are the same between the general population and the residents of Salt Lake City. H1: The distributions of hair colors are NOT the same between the general population and the residents of Salt Lake City. a. The observed frequencies are recorded below. Fill in the expected value, round answers to at least 4 decimal places. 27.524 Red, Gray, White or Other 35 Hair Color Observed Expected 79 4.264 I Dark Brown or Black 728 0" 100.266 V Brown 133 0" 60.946 V Blonde 87 o'5 o' b. The degree of freedom = 0\" c. The test-statistic for this data = 29.3835/ 0" d. The p-value for this sample = Enter an integer or decimal number e. The p-value is less than {or equal to) alpha V a 0' f. Based on this, we should reject the null hypothesis V o" g. As such, the final conclusion is that... 9 Based on the sample data, there is sufficient evidence to conclude that the distributions of hair color is not the same between the general population and the residents of Salt Lake City at the a = 0.01 significance level. Based on the sample data, there is not sufficient evidence to conclude that the distributions of hair color is not the same between the general population and the residents of Salt Lake City at the a = 0.01 significance level. 0\" Submit