Brand 1 Brand 2 7.9 10.1 7.4 9.3 5.7 8.8 4.5 6.4 7.2 6.2 9.6 5.3 6.8 7.5 7.4 5 6.9 4.9 6.6 6.8 6.1 9.5 9.8 6.4 7.2 8.3 5.7 8.6 7.5 7.9 7 6.1 7.1 8.3 5.7 8.9 5 8.2 4 8.4 7.9 7.1 6.8
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Using the given data sets
a.Conduct a hypothesis test at a significance level of 5% to see if there is a statistically significant difference in the average oil levels between Brand 1 and Brand 2.
b. If the manufacturers of brand 1 assert that their product has a higher average oil content than brand 2, test at the 5% level of significance, whether their claim can be supported by the sample evidence
Show the workings for the normal statistics terms such mean,standard deviation,variance,t-test,p-value using t statistical tables without using Python,Excel or any software
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- Consider the following two datasets:Dataset 1 Dataset 21 9 5 51 9 5 51 9 5 51 9 5 51 9 5 5(a) Compute the mean and range of each dataset.(b) Which dataset appears to have the less variation? (c) Compute the sample standard deviation of each dataset.(d) Which measure of variation (range or standard deviation) better distinguishes the variation of data in the 2 datasets? Explain your answer.Listed in the data table are IQ scores for a random sample of subjects with medium lead levels in their blood. Also listed are statistics from a study done of IQ scores for a random sample of subjects with high lead levels. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.01 significance level.Consider the data below. Three random samples in different cities were selected. Water use per household per day were measured. Test the claim that the samples come from populations with the same mean. Assume all requirements have been met. Use a 5% level of significance. 1. Identify the tail of the test. [ Select ] 2. Find the P-value. [ Select ] 3. Will the null hypothesis be rejected? [ Select ] 4. Do the populations appear to have the same mean? [ Select ] Sample Data City 1 City 2 City 3 70 66 66 70 64 66 55 45 54 60 41 61 65 58 65 45 44 65 55 46
- Refer to the accompanying data table, which shows the amounts of nicotine (mg per cigarette) in king-size cigarettes, 100-mm menthol cigarettes, and 100-mm nonmenthol cigarettes. The king-size cigarettes are nonfiltered, while the 100-mm menthol cigarettes and the 100-mm nonmenthol cigarettes are filtered. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only the king-size cigarettes are not filtered, do the filters appear to make a difference? Click the icon to view the data table of the nicotine amounts. Determine the null and alternative hypotheses. C Nicotine amounts (mg) Ho: H₁: Find the F test statistic. F= (Round to four decimal places as needed.) Find the P-value using the F test statistic. P-value= (Round to four decimal places as needed.) What is the conclusion for this hypothesis test? O A. Reject Ho. There is insufficient evidence to warrant rejection of the claim that the three…Refer to the accompanying data table, which shows the amounts of nicotine (mg per cigarette) in king-size cigarettes, 100-mm menthol cigarettes, and 100-mm nonmenthol cigarettes. The king-size cigarettes are nonfiltered, while the 100-mm menthol cigarettes and the 100-mm nonmenthol cigarettes are filtered. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only the king-size cigarettes are not filtered, do the filters appear to make a difference? E Click the icon to view the data table of the nicotine amounts. Nicotine amounts (mg) ..... Determine the null and alternative hypotheses. Но King-Size 100-mm Menthol 100-mm Nonmenthol 9 Brand Nicotine (mg) Brand Nicotine (mg) Brand Nicotine (mg) H1 1 1.5 1 1.2 1 0.9 1.0 2 1.0 2 1.2 Find the F test statistic. 3 1.0 3 1.1 3 0.4 4 1.2 4 0.8 4 1.2 F = (Round to four decimal places as needed.) 5 1.4 1.3 1.1 6 1.3 1.4 0.7 Find the P-value using the F test…Refer to the accompanying data table, which shows the amounts of nicotine (mg per cigarette) in king-size cigarettes, 100-mm menthol cigarettes, and 100-mm nonmenthol cigarettes. The king-size cigarettes are nonfiltered, while the 100-mm menthol cigarettes and the 100-mm nonmenthol cigarettes are filtered. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only the king-size cigarettes are not filtered, do the filters appear to make a difference? LOADING... Click the icon to view the data table of the nicotine amounts. Nicotine amounts (mg) Dialog content starts King-Size 100-mm Menthol 100-mm Nonmenthol Brand Nicotine (mg) Brand Nicotine (mg) Brand Nicotine (mg) 1 1.3 1 0.9 1 0.2 2 1.2 2 1.0 2 1.1 3 1.0 3 1.2 3 0.6 4 1.1 4 0.9…
- A kilo restaurant implemented a change in the composition and presentation of its dishes. We want to assess whether the average weight of meals served is greater after the changes, compared to the previous average, which was 640. For this purpose, the weights of dishes from a random sample of 10 customers were taken. The average weight of dishes in the sample was 656 and the variance 144. Use a statistical test for the evaluation. Adopt a significance level of 10%. a. What is the value of the test statistic? b. What range of values is the p-value in? c. At the 10% significance level, can you reject the null hypothesis?Listed in the accompanying table are heights (in.) of mothers and their first daughters. The data pairs are from a journal kept by Francis Galton. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Use a 0.05 significance level to test the claim that there is no difference in heights between mothers and their first daughters. Mother 64.0 66.0 63.0 62.0 66.5 66.0 65.0 60.0 67.0 63.0 Daughter 67.0 66.5 70.5 66.0 61.0 66.0 65.5 65.0 67.0 65.0 In this example, Hd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the daughter's height minus the mother's height. What are the null and alternative hypotheses for the hypothesis test? Ho: Ha = 0 in. H₁ Hd 0 in. (Type integers or decimals. Do not round.) Identify the test statistic. t= (Round to two decimal places as needed.)A kilo restaurant implemented a change in the composition and presentation of its dishes. We want to assess whether the average weight of meals served is greater after the changes, compared to the previous average, which was 640. For this purpose, the weights of dishes from a random sample of 10 customers were taken. The average weight of dishes in the sample was 656 and the variance 144. Use a statistical test for the evaluation. Adopt a significance level of 10%. a. What is the distribution of the test statistic? b. What kind of alternative hypothesis? c. What is the test's critical value (the value that defines the critical region), on the scale of the test statistic? (If the test is bilateral, enter only one of the values.)
- Kenneth, a competitor in cup stacking, claims that his average stacking time is 8.2 seconds. During a practice session, Kenneth has a sample stacking time mean of 7.8 seconds based on 11 trials. At the 4% significance level, does the data provide sufficient evidence to conclude that Kenneth's mean stacking time is less than 8.2 seconds? Accept or reject the hypothesis given the sample data below. H0:μ=8.2 seconds; Ha:μ<8.2 seconds α=0.04 (significance level) z0=−1.75 p=0.0401 Select the correct answer below: a. Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. b. Reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. c. Reject the null hypothesis because the value of z is negative. d. Reject the null hypothesis because |−1.75|>0.04. e. Do not reject the null hypothesis because |−1.75|>0.04.A two-sample hypothesis test is comparing the averages of the following populations. Population 1 is the salary of female employees and Population 2 is the salary of male employees. A hypothesis test was conducted to see if the average salary of males is greater than the average salary of females. Using the following as the output of the test, state the P-value and interpret the results in context to the problem. Use a significance level of 5% Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Females Males 65,852.00 89,562.00 1,003.00 1,025.00 45 30 0 37 -1.26 0.1200 1.3300 0.2400 1.2800 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph Arial 10pt EEVA V Tx XQ5 二 三 ||||| WORDS POWERED BY TINYTwo brands of batteries are tested, and their voltages are compared. The summary statistics follow. For sample 1, the sample size is 27; the population standard deviation is 0.3 volts and the mean is 9.2 volts. For sample 2, the sample size is 30; the population standard deviation is 0.1 volts and the mean is 8.8 volts. Is the mean of sample 1 smaller than the mean of sample 2? Using a significance level of 0.05. a) Identify the claim and state the hypotheses. b) What is the test statistics? Find the critical values (s). c) Make the decision to reject or not reject the null hypothesis and explain why. d) Graph your decision and include all the values. That is, the mean, the standard deviation, the critical value(s), the rejection region. e) Set up the formula with the correct numbers for the 95% confidence interval of the mean number of jobs.