Question

In: Math

1. A researcher is testing the claim that adults consume an average of at least 1.85...

1. A researcher is testing the claim that adults consume an average of at least 1.85 cups of coffee per day. A sample of 35 adults shows a sample mean of 1.70 cups per day with a sample standard deviation of 0.4 cups per day. Test the claim at a 5% level of significance. What is your conclusion?

2. A government Bureau claims that more than 50% of U.S. tax returns were filed electronically last year. A random sample of 150 tax returns for last year contained 86 that were filed electronically. Test the Bureau's claim at a 5% level of significance. What is your conclusion? Report the p-value for this test.

3. A major automobile company claims that its New electric-powered car has an average range of more than 100 miles. A random sample of 50 new electric cars was selected to test the claim. Assume that the population standard deviation is 12 miles. A 5% level of significance will be used for the test.

A) What would be the consequences of making a Type II error in this problem?

B) Compute the Probability of making a Type II error if the true population means is 105 miles.

C) What is the maximum probability of making a Type I error in this problem?

Please Note: A hypothesis test answer must contain: a Null and an Alternate Hypothesis, a computed value of the test statistic, a critical value of the test statistic, a Decision, and a Conclusion.

Expert Solution

1. A researcher is testing the claim that adults consume an average of at least 1.85 cups of coffee per day. A sample of 35 adults shows a sample mean of 1.70 cups per day with a sample standard deviation of 0.4 cups per day. Test the claim at a 5% level of significance. What is your conclusion?

Answer)

Null hypothesis Ho : u >= 1.85

Alternate hypothesis Ha : u < 1.85

As the population s.d is unknown here, we will use t distribution to estimate the test

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (1.7 - 1.85)/(0.4/√35) = -2.219

Degrees of freedom is = n-1 = 34

For 34 df and -2.219 test statistics

P-value from t distribution is = 0.0166

As obtained P-value is less than 0.05 (5%) given significance level

We reject the null hypothesis that u >=1.85

So we do not have enough evidence to support the claim that adults consume an average of at least 1.85 cups of coffee per day.

milcah answered 11 months ago

A researcher is testing the claim that adults consume an average of at least 1.85 cups...

A researcher is testing the claim that adults consume an average of at least 1.85 cups of coffee per day. A sample of 35 adults shows a sample mean of 1.70 cups per day with a sample standard deviation of 0.4 cups per day. Test the claim at a 5% level of significance. What is your conclusion? *Please explain each step, I just don't get it

Suppose that 55% of all adults regularly consume coffee, 45% regularly consume car- bonated soda, and 70% regularly consume at least one of these two products.

Suppose that 55% of all adults regularly consume coffee, 45% regularly consume car- bonated soda, and 70% regularly consume at least one of these two products. (a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? (b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?

A researcher wishes to test claim that that the average cost of a coke in Mexico...

A researcher wishes to test claim that that the average cost of a coke in Mexico is different than the average cost for a coke in Russia. The cost is measured in US Dollars. Sample data are provided below. Test the claim using α=0.10. Mexico Russia X ¯ 1 =1.26 s 1 =0.11 n 1 =14 X ¯ 2 =1.52 s 2 =0.09 n 2 =14 State the claim: H 0 μ 1 H 1 μ 1≠ μ 2 claim...

In a pilot study for testing the "truth" to the theory that, on average, U.S. adults...

In a pilot study for testing the "truth" to the theory that, on average, U.S. adults gain weight between Thanksgiving and January, a research team looked at responses from 8 randomly selected U.S. adults. The subjects were weighed (lb) on the day before Thanksgiving and again on January 3rd The raw data are found in Table 1. Let α = 0.05 Table 1: Weights (lb) before Thanksgiving and on Jan. 3rd for 8 U.S. adults Pre-Thanksgiving 156.4 153.0 154.1 151.3...

researcher wishes to test the claim that the average weight of an adult elephant is 12500...

researcher wishes to test the claim that the average weight of an adult elephant is 12500 pounds. The researcher collected a sample of 33 adult elephants. The sample average for the weight of the elephants was 12200 pounds. The population standard deviation is believed to be 720 pounds. With alpha = 0.06, is there enough evidence to reject the claim. a) Is this a test that uses, z-scores, t-scores, or chi-squared values? b) [2 points] Does this problem involve proportions?...

Do US adults consume an average of more than 75 grams of fat per day? According...

Do US adults consume an average of more than 75 grams of fat per day? According to a study of 600 adults in a scientifically designed study, the sample mean was 77.23 grams with sample standard deviation 33.47 grams. Do all the steps of a hypothesis test using normal theory methods, including finding the p-value, and write the conclusion in context.

Adults around the world watch on average 4 hours of TV a day. A researcher thinks...

Adults around the world watch on average 4 hours of TV a day. A researcher thinks that Americans watch less TV than the international average. He finds 25 Americans who watch 3 hours of television a day on average, with a standard deviation of 2 hours. Using an Alpha = .05, test this hypothesis. BE SURE TO ANSWER ALL PARTS OF THE QUESTION AND SHOW YOUR WORK WHEN YOU CAN. a) What is the appropriate test? b) State the null...

Question 3: Hypothesis Testing about the population mean (μ) A researcher claims that the average...

Question 3: Hypothesis Testing about the population mean (μ) A researcher claims that the average weekly spending for lunch by commuting students in US colleges is usually higher in winter semester than the of average of $30 in the prior fall semester. To verify this claim a sample of 100 commuting students were randomly selected in spring semester and their average weekly spending was reported as $32.5. From historical experience the population standard deviation of weekly spending by commuting...

1a.Suppose that 60% of all adults regularly consume coffee, 40% regularly consume carbonated soda, and 65%...

1a.Suppose that 60% of all adults regularly consume coffee, 40% regularly consume carbonated soda, and 65% regularly consume at least one of these two products. (a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? (b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products? 1b. An insurance company offers four different deductible levels—none, low, medium, and high—for its homeowner's policyholders and three...

A health researcher read the claim that a 200-pound male can burn more than an average of...

A health researcher read the claim that a 200-pound male can burn more than an average of 524 calories per hour playing tennis with a standard deviation of 45.9 calories. 37 males were randomly selected and the mean number of calories burnt per hour was 534.8. Test at 5% of level of significance whether the claim is correct? (Hint: Right Tailed Test) State Null and Alternate Hypotheses. Apply test. Write your conclusion using critical value approach and p value approach. Construct a...