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- t Test for TWO DEPENDENT (Related) SAMPLES (Show all work) A manufacturer of a gas additive claims that it improves gas mileage. A random sample of 40 drivers tests this claim by determining their gas mileage for a full tank of gas that contains the additive (X1) and for a full tank of gas that does not contain the additive (X2). The sample mean difference D-Bar equals 2.12 miles (in favor of the additive) and the estimated standard error equals 1.50 miles. Test the Null Hypothesis with t, using the .05 Level of significance and construct a 95 percent confidence interval (whether you reject OR retain the Null Hypothesis)An engineer working for a large agribusiness has developed two types of soil additives he calls Add1 and Add2. The engineer wants to test whether there is any difference between the two additives in the mean yield of tomato plants grown using these additives. The engineer studies a random sample of 11 tomato plants grown using Add1 and a random sample of 13 tomato plants grown using Add2. (These samples are chosen independently.) The plants grown with Add1 have a sample mean yield of 139 tomatoes with a sample variance of 510. The plants grown with Add2 have a sample mean yield of 151.2 tomatoes with a sample variance of 2178.8. Assume that the two populations of yields are approximately normally distributed. Can the engineer conclude, at the 0.05 level of significance, that there is a difference between the population mean of the yields of tomato plants grown with Add1 and the population mean of the yields of tomato plants grown with Add2? Perform a two-tailed test. Then complete the…How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 56 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 14°C. (a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.) lower limit °C upper limit °C (b) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, do you expect that the balloon will…
- In statistical terms how do we determine whether or not the model is significant? O The t tests and the F-tests are statistically insignificant O The F-tests are significant while the t tests are not. The t tests and the F-tests hypotheses are rejected O The standard error is lowTest the null hypothesis that ros has no effect on salary against the alternative that ros has a positive effect. Carry out the test at the 10% significance level. Hint use t distribution with df = ∞,A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of n=1100n=1100 registered voters and found that 570 would vote for the Republican candidate. Let pp represent the proportion of registered voters in the state who would vote for the Republican candidate.We test H0:p=.50H0:p=.50Ha:p>.50Ha:p>.50 (a) What is the zz-statistic for this test? (b) What is the P-value of the test?
- I3D I3D 4. The table below gives the number of US Senators, from each party, spending federal dollars in each of three spending classes. The table is set up to help you calculate x? so there are blanks provided in addition to the data: a. Fill in the contingency tables for the Expected Frequencies (work to 2 decimal places): Spending Less than 6 to 11 Billion More than Party 6 Billion 11 Billion Republican 8 - 15 - 22 Democrat 12 - 16 - %3D - 6 b. Calculate the differences between the observed frequencies and the expected frequencies and fill in above. C. Calculate x and the degrees of freedom. Ans. Ans. d. Use this information to do a Chi Squared test to determine the validity of the claim that federal spending is independent of political party at the a =.05 level. Use the worksheet on the following page.spss/minitabWhich type of t-test is best for the following variables:(a) Test scores of Section A51 at start of Semester (b) Test scores of Section A51 at end of Semester Paired Samples t-test Independent Samples t-test None. The variables are both discrete. None. The variables are both continuous. 8
- Q 3: Al Matra LLC has recently hired Mr. Musab, a professional market researcher. Mr. Musab is interested to find out relationship between cost incurred and revenue earned by the company. He collected the data of last 7 years from the accounts department, but he is confused about the method which can find out the relationship. Revenue Cost Incurred Earned Year (OMR in (OMR in Millions) Millions) 2013 20 2014 10 22 2015 9 22 2016 18 2017 11 20 2018 12 24 2019 10 25 a) Find out the correlation value and give interpretation of the result b) If correlation value is 1.25, discuss the result analytically.true if the statement is unconditionally TRUE and false if otherwiseTest the null hypothesis that ros has no effect on salary against the alternative ros has a positive effect at 10% significance level. Use T distribution with df= infinity
