The average weight of 2-year old toddlers is 27 pounds. Social workers in a state are concerned about the weights of 2-year old toddlers who are in foster care. They think the average weight of these toddlers is less than the healthy weight of 27 pounds. They collect the weights of 52 toddlers (2-years old) and they found that the test statistic for the appropriate hypothesis was t = -2.8. Does this measurements provide enough evidence for the social workers claim at the 5% significance level?
Question
The average weight of 2-year old toddlers is 27 pounds. Social workers in a state are concerned about the weights of 2-year old toddlers who are in foster care. They think the average weight of these toddlers is less than the healthy weight of 27 pounds. They collect the weights of 52 toddlers (2-years old) and they found that the test statistic for the appropriate hypothesis was t = -2.8. Does this measurements provide enough evidence for the social workers claim at the 5% significance level?
Solution
To answer this question, we need to understand the concept of a t-test and the significance level in hypothesis testing.
Step 1: State the hypotheses. The first step is to state the null hypothesis and the alternative hypothesis.
Null hypothesis: The average weight of 2-year old toddlers in foster care is 27 pounds. Alternative hypothesis: The average weight of 2-year old toddlers in foster care is less than 27 pounds.
Step 2: Formulate an analysis plan. For this analysis, the significance level is defined as 0.05 (5%). The degrees of freedom is 52-1=51.
Step 3: Analyze sample data. Using sample data, we calculate the pooled sample standard deviation and the standard error. Using those measures, we compute the t-score test statistic (t = -2.8).
Step 4: Interpret the results. We use the t-distribution table to find the critical value for a one-tailed test at a significance level of 0.05 with 51 degrees of freedom, which is approximately 1.675. Since our test statistic (-2.8) is less than the critical value (-1.675), we reject the null hypothesis.
So, the measurements provide enough evidence to support the social workers' claim that the average weight of 2-year old toddlers in foster care is less than 27 pounds at the 5% significance level.
Similar Questions
Based on their records, a hospital claims that the proportion, p, of full-term babies born in the community that weigh more than 7 pounds is 44%. A pediatrician who works with several hospitals in the community would like to verify the hospital's claim. In a random sample of 185 babies born in the community, 77 weighed over 7 pounds. Is there enough evidence to reject the hospital's claim at the 0.01 level of significance? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H_0 and the alternative hypothesis H_1. (b) Determine the type of test statistic to use. (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we reject the claim that the proportion of full-term babies born in the community that weigh more than 7 pounds is 44%?
A doctor claims that the mean weight of babies delivered at her hospital is 6.1kg. A Statistician takes a sample of 10 babies and obtains the following weights: 1.2, 1.4, 1.1, 2.3, 4.2, 0.7, 1.9, 1.1, 4.2, 8.2. Test the doctor\'s claim at 95% level of significance.
Babies: According to a recent report, a sample of 240 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is =σ5.1 pounds.Part: 0 / 30 of 3 Parts CompletePart 1 of 3(a) Construct an 80% confidence interval for the mean weight of all one-year-old baby boys in the United States. Round the answer to at least one decimal place.An 80% confidence interval for the mean weight in pounds of all one-year-old baby boys in the United States is <<μ.
Watch your weight: A study published in 2008 reported that the mean weight of men aged 40-59 was 89.3 kg. Another study, published in 2016, reported that a sample of 192 men aged 40-59 had an average weight of 87 kg. Assume the population standard deviation is =σ14.2 kg. Can you conclude that the mean weight of men aged 40-59 is lower in 2016 than in 2008? Use the =α0.05 level of significance.Part: 0 / 50 of 5 Parts CompletePart 1 of 5(a) State the appropriate null and alternate hypotheses.H0: H1: The hypothesis test is a ▼left-tailed test.
In a two-tailed hypothesis test situation, the test statistic is determined to be t = -2.032. The sample size is 35. The p-value for this test is-.05.+.05.-.10.+.10.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.