It has been found that the household's monthly grocery expenses in February 2022 follows a normal distribution with an average expense of 2700 USD and a standard deviation of 200 USD. Find the probability that a random sample of 25 observations will have a sample variance S^2 greater than 300.
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- An automotive corporation claimed that their sedan brand of car can travel an average mean of 35 km in a liter of gasoline and if the standard deviation of 2 kilometers. The consumers made a test using 64 cars of the same brand and it had resulted to 32 kilometers for a liter of gasoline. Which claim would be accepted at 5% level of significance at 1 tailed test?Is there any difference in the variability in golf scores for players on a women's professional golf tour and players on a men's professional golf tour? A sample of 20 tournament scores from events in a tour for women showed a standard deviation of 2.4683 strokes, and a sample of 30 tournament scores from events in a tour for men showed a standard deviation of 2.2117. Conduct a hypothesis test for equal population variances to determine if there is any statistically significant difference in the variability of golf scores for male and female professional golfers. Use α = 0.10. A. State the null and alternative hypotheses. 1.H0: σ12 ≤ σ22 Ha: σ12 > σ22 2. H0: σ12 = σ22 Ha: σ12 ≠ σ22 3. H0: σ12 > σ22 Ha: σ12 ≤ σ22 4. H0: σ12 ≠ σ22 Ha: σ12 = σ22 B. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = C. State your conclusion. 1. Do not reject H0. We cannot…A random variable of 25 packs of powdered milk showed a mean content of 237 grams with a standard deviation of 8.56 grams while a sample of 20 packs of another brand of powdered milk showed a mean content of 240 grams with a standard deviation of 9.75 grams. Using a 0.05 level of significance, is there significant difference in the mean content of the two brands of powdered milk? Assumed variances are equal.
- A researcher randomly sampled 100 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The summary results are given below: Male MBA Graduates: Sample mean = $85500, Sample standard deviation = 10000, Sample size = 50 Female MBA Graduates: Sample mean = $78000, Sample standard deviation = 8000, Sample size = 50 Assuming that the populations are normally distributed and the population variances from both populations are equal, is there evidence that the average starting salary of the male MBA graduates is higher than the average starting salary of the female MBA graduates? Use a 0.05 level of significance. (a) State the null and alternative hypothesis for this problem. (b) What is the value of the pooled-variance tSTAT test statistic for this problem? (c) Using the level of…A recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching television among the single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean number of minutes spent watching television was 48.4 minutes, with a standard deviation of 18.1 minutes. At the 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching television together? There were 15 single-earner and 12 dual-earner couples studied. Hint: For the calculations, assume the single-earner as the first sample. Is this a one-tailed or a two-tailed test? multiple choice 1 One-tailed test. Two-tailed test. State the decision rule. (Round your answer to 3 decimal places.) Compute the value of the test statistic. (Round your answer to 3 decimal…A New York Times article noted that the mean life span for 6 male symphony conductors was 80.4 years with standard deviation of 6.9 years. That is in contrast to the mean of 67.1 years for males in the general population. Use a 0.5 significance level to test the claim that male symphony conductors have a mean life span that is greater than 67.1 years.
- A manufacturing firm has been averaging 18.3 orders per week for several years.however, during a recession, orders appear to have slowed. Suppose the firm's production manager randomly samples 32 weeks and finds a sample mean of 15.6 orders, with a sample standard deviation of 2.3 orders. Test to determine whether the average number of orders is down by using a = 0.10.The Food and Nutrition Research Institute (FNRI) of the Department of Science and Technology (DOST) recommends that children 1 to 3 years old have a 1070 kilocalories (kcal) of energy intake. A random sample of 78 children 1 to 3 years old from a certain region reported an average energy intake of only 440 kcal with a standard deviation of 190 kcal. Can you conclude that the mean energy intake of children 1 to 3 years old from this region is significantly lower than the FNRI recommendation of 1070 kcal? Use a 5% level of significance.A random sample of 100 recorded deaths in United States during the past year showed that an average lifespan of 70.8 years. Assuming a population standard deviation of 8.7 years, does this deem to indicate that the mean lifespan today is greater than 70 years? Use a 0.05 level of significance.
- From a random sample of six students in an introductory finance class that uses group-learning techniques, the mean examination score was found to be 76.12 and the sample standard deviation was 2.53. For an independent random sample of nine students in another introductory finance class that does not use group learning techniques, the sample mean and standard deviation of exam scores were 74.61 and 8.61, respectively. Estimate with 95% confidence the difference between the two population mean scores; do not assume equal population variances.A recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching television among the single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean number of minutes spent watching television was 48.4 minutes, with a standard deviation of 18.1 minutes. At the .01 significance level, can we conclude that the single-earner couples on average spend more time watching television together? There were 15 single-earner and 12 dual-earner couples studied.The monthly expenditure of a family was observed to be normally distributed with mean ofGhc400 and standard deviation of Ghc20. If Ghc450 is budgeted for a month, what is theprobability that the actual expenditure willa. be less than the budgeted amount?b. exceed the budgeted amount?