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PilotLPTM [1.2K]
3 years ago
15

In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To

determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7.
At the α = 0.05 level of significance, does the nutritionist have enough evidence to reject the writer’s claim?

a. No
b. Yes
c. Cannot determine
Mathematics
1 answer:
Ymorist [56]3 years ago
8 0

Answer:

t=\frac{78-75}{\frac{7}{\sqrt{20}}}=1.917  

The degrees of freedom are given by:

df= n-1 = 20-1=19

The p value would be given by:

p_v =2*P(t_{19}>1.917)=0.0704  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 75 and the best option would be:

a. No

Step-by-step explanation:

Information given

\bar X=78 represent the sample mean

s=7 represent the sample standard deviation

n=20 sample size  

\mu_o =75 represent the value that we want to test  

\alpha=0.05 represent the significance level for the hypothesis test.  

t would represent the statistic

p_v represent the p value

Hypothesis to test

We want to check if the true mean is different from 75, the system of hypothesis would be:  

Null hypothesis:\mu =75  

Alternative hypothesis:\mu \neq 75  

The statistic is given by:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

Replacing we got:

t=\frac{78-75}{\frac{7}{\sqrt{20}}}=1.917  

The degrees of freedom are given by:

df= n-1 = 20-1=19

The p value would be given by:

p_v =2*P(t_{19}>1.917)=0.0704  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 75 and the best option would be:

a. No

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2. Maria is monitoring the temperature of
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Here, we are required to determine after how many minutes will the two substances be at the same temperature.

The equation of when the two substances will be at the same temperature and the solution are as follows;

(a) The equation is 96.2 + 1.5(x) = 98.5 + 0.8(x).

(b) The solution is, x = 3.285minutes.

For substance A which is currently at 96.2° and rising at 1.5° each minute; It's temperature after x minutes is given as;

  • T(a) = 96.2 + 1.5(x)

For substance B which is currently at 98.5° and rising at 0.8° each minute; It's temperature after x minutes is given as;

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The equation is therefore;.

96.2 + 1.5(x) = 98.5 + 0.8(x)

(b) To determine the solution;

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Read more:

brainly.com/question/20248109

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A hat is marked down 45% and its new price is $69. What was the original price rounded to the nearest cent?
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Answer:

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Step-by-step explanation:

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$69 x 0.55 = 37.95

$69 + 37.95 = $106.95

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5 0
3 years ago
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