Question

The CDC publishes charts on Body Mass Index (BMI) for boys and girls of different ages. Based on the chart for girls, the mean BMI for 6-year-old girls is listed as 15.8 kg/m2. The data from which the CDC charts were developed is old and there is concern that the mean BMI for 6 year olds girls has increased.

The BMI’s from a current random sample of 50 6-year-old girls is attached in a list on the next page. Use this data of current six-year girls to test the claim that the mean BMI for current girls is greater than 15.8 (thus, testing that the mean BMI for six-year-old girls has increased since the chart was made).

1. State the claim, null hypothesis, and alternate hypothesis in symbols.

Claim:

H0 : ?

H1: ?

2. Copy and paste the sample of 50 BMI’s into stat crunch. Calculate the mean and standard deviation for the sample.

Mean = ?

Standard deviation = ?

3. Use stat crunch to run a hypothesis test for mean. Go to stat > t-stats > one-sample > with data. (you can also choose “with summary” and enter your sample mean and sample standard deviation from part 2)

**Enter your information for your null hypothesis and alternative hypothesis (make sure to select the appropriate inequality sign for your alternate hypothesis).

Record your p-value: ____________

4. Based on your p-value, do you reject your null hypothesis or fail to reject your null hypothesis? Use a 0.05 significance level.

5. Based on your answer #3 and #4, does the sample data provide sufficient evidence that the mean BMI for 6-year-old girls has increased? Explain.

Math 1740 92 Week 7 – Hypothesis Testing Assignment

24.5 16.3 15.7 20.6 15.3 14.5 14.7 15.7 14.4 13.2 16.3 15.9 16.3 13.5 15.5 14.3 13.7 14.3 13.7 16 14.2 17.3 19.5 22.8 16.4 15.4 18.2 13.9 17.6 15.5 17.8 15.2 18.9 17.7 13.7 21 18.4 14.7 16.9 13.8 14.9 14.1 17.6 13.6 22.6 15.1 18.1 16.8 14.2 13.3

Answer #1

4. The CDC publishes charts on Body
Mass Index (BMI) percentiles for boys and girls of different ages.
Based on the chart for girls, the mean BMI for 6-year-old girls is
listed as 15.2 kg/m2. The data from which the CDC charts were
developed is old and there is concern that the mean BMI for 6-year
old girls has increased. The BMIs of a random sample of 30
6-year-old girls are given below.
24.5
16.3
15.7
20.6
15.3
14.5
14.7...

Q7 The mean body mass index (BMI) for boys of age 12 years is
23.6 kg/m2. An investigator wants to test if the BMI is
higher in 12-year-old boys living in New York City. How many boys
are needed to ensure that a two-sided test of hypothesis has 80%
power to detect a difference in BMI of 2 kg/m2? Assume
that the standard deviation in BMI is 5.7 kg/m2.
Q8 An investigator wants to design a study to estimate the...

The body mass index (BMI) of a person is the person’s weight
divided by the square of his or her height. It is an indirect
measure of the person’s body fat and an indicator of obesity.
Results from surveys conducted by the Centers for Disease Control
and Prevention (CDC) showed that the estimated mean BMI for US
adults increased from 25.0 in the 1960–1962 period to 28.1 in the
1999–2002 period. [Source: Ogden, C., et al. (2004). Mean body
weight,...

Sample Statistic
Value of sample statistic
Sample mean () Body Mass Index (BMI)
21.65
Sample standard deviation (s) of Body Mass Index (BMI)
4.33
Sample size
92
(13 points) You will use information about the body
mass index (BMI) variable for the sample of adolescent girls to
perform a hypothesis test. You will test the claim that the mean
BMI for all adolescent girls is 21.0.
The null hypothesis is H0 : µ = 21.0. State the
alternate hypothesis for...

USE EXCEL ONLY PLEASE
Using the data on the weight of a particular small animal find a
simple random sample of size 10, and a systematic sample of size
10. If you use the Data Analysis Tool Pack, include screenshots of
your settings in your submitted work. Find the mean and standard
deviations of your sample
Weight
16.5
12.2
12.0
10.6
9.8
9.3
12.4
14.2
13.1
10.9
12.8
16.1
13.5
14.1
12.5
10.7
13.1
15.3
12.7
12.1
15.9
14.7
15.3...

A cable internet provider claims that users can download data at
an average speed of 15 megabits per second (Mbps). You are a
customer of this ISP, and you decide to test this claim. You
perform 17 tests where you measure your connection speed (in Mbps),
and you find the data below. Note that you only care if your
connection speed is significantly less than advertised!
14.1, 15.0, 14.2, 15.4, 15.1, 13.7, 15.8, 13.4, 14.8, 15.2,
15.5, 13.2, 12.8, 16.0,...

Table (every row is a pencil and its corresponding data) :
Ash
Porosity
Outer Diameter
Strength
Location
42.2
12.9
0.087
1.25
1
43.8
13.7
0.09
1.2
1
42.1
15.6
0.087
0.85
1
42
13.3
0.086
1.15
1
45
12.2
0.088
1.55
1
42.5
14.3
0.085
1
1
41.9
13.1
0.085
1
1
42.4
13.8
0.086
1.05
1
41.9
14.4
0.085
1.15
1
42.1
15.5
0.086
0.9
1
42.2
12.7
0.087
1.3
1
43.4
13.4
0.089
1.2
1
41.9
12.9
0.084...

A gardener plants 300 sunflower seeds (of a brand called
KwikGrow) and, after 2 weeks, measures the seedlings’ heights (in
mm). These heights are recorded in the file Sunflower.csv. He is
interested in testing whether the mean height of sunflowers grown
from KwikGrow seeds is greater than 33 mm two weeks after planting.
He decides to conduct a hypothesis test by assuming that the
sampling distribution of the sample mean has a normal distribution.
For the purposes of this question,...

A gardener plants 300 sunflower seeds (of a brand called
KwikGrow) and, after 2 weeks, measures the seedlings’ heights (in
mm). These height are: 38.6 39.1 50.4 49.2 46.2 0 43.1 49.6 16.1
17.9 11.6 50.2 36.5 50.6 40.3 36.3 14.3 40.8 12.1 43.7 47.2 49.9
37.9 49.1 53 47.7 13.8 38.3 49.2 50.6 49.6 52.3 19.8 12.8 46.9 35.3
38.7 39.3 12.4 51.9 36.9 20.8 51.7 44.3 49.1 10.7 14.9 48.2 14.8 38
41.4 39.4 11.9 13.8 0 35.1...

3. Should the CBC hire stars for their movies? To answer this
question, run a hypothesis test to see if there is a significant
difference between the ratings of movies with stars versus movies
without stars. Use the data for CBC movies only. Use 95%
confidence. Answer the following: a. What are the null and
alternative hypotheses (state in full sentences)? b. Run the test
using Excel and include the output table. Use a t-test assuming
equal variances. c. What...

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