chuck jogged the same distance on tuesday and friday, but jogged 8 miles on sunday . if he ran a total of 2o miles, how many mil
1 answer:
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Answer:
Step-by-step explanation:
Hello!
A pilot study was conducted to test if three food rewards are equally appealing to the participants.
Of 60 participants surveyed:
16 preferred cupcakes (CC)
26 preferred candy bars (CB)
18 preferred dried apricots (DA)
If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3
1.
The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. Where k= number of categories of the variable.
For this example the statistical hypotheses are:
H₀: P(CC)=P(CB)=P(DA)= 1/3
H₁: At least one of the proportions isn't equal to the others.
2.
To calculate the expected frequencies for each category you have to use the formula: where Pi represents the theoretical proportion for the i category, stated in the null hypothesis.
3.
The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:
Assuming α: 0.05
The rejection region is then X²₂ ≥ 7.378
4.
I hope this helps!
Answer:
2. b : l
3. 20cm
4. 49
5.
Step-by-step explanation:
<u>Solution 2:</u>
Let cylinder is rolled along 'l':
Height of cylinder , h = length of rectangle = l
Perimeter of base = b
Let 'r' be the radius of cylinder's base:
Volume of a cylinder is given as:
Putting the values:
Let cylinder is rolled along 'b':
Height of cylinder , h = length of rectangle = b
Perimeter of base = l
Let 'r' be the radius of cylinder's base:
Volume of a cylinder is given as:
Putting the values:
Taking ratio:
Solution 3:
Rectangle is rolled along its length to make a cylinder, so height will be equal to its length.
height of cylinder = 20 cm
Solution 4:
Side of square = 7 cm
Height of cylinder =Side of square = 7 cm
7 cm will be the circumference of the circle.
i.e. = 7 cm
Curved surface area of a cylinder:
Putting the above values:
CSA = 7 7 = 49
Solution 5:
As calculated in above step:
CSA = 7
7 = 49
Total surface area =
Calculating value of r:
= 7 cm
Total surface area =
Ratio of TSA: CSA is