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SOVA2 [1]
3 years ago
15

a normal distribution with a mean of 25 minutes with a population standard deviation of 5 minutes. The store manager sampled 100

customers and found that the mean waiting time was 24.25 minutes. At the 0.01 significance level, test if the mean waiting time is less than 25 minutes.
Mathematics
1 answer:
sergiy2304 [10]3 years ago
4 0

Answer:

z=\frac{24.25-25}{\frac{5}{\sqrt{100}}}=-1.5      

The p value for this case would be given with this probability:

p_v =P(z  

For this case since the p value is higher than the significance level of 0.01 we have enough evidence to fail to reject the null hypothesis and we don't have enough evidence to conclude that the true mean is significantly less than 25 min.

Step-by-step explanation:

Information given

\bar X=242.5 represent the sample mean      

\sigma=5 represent the population deviation

n=100 sample size      

\mu_o =25 represent the value to check

\alpha=0.01 represent the significance level

z would represent the statistic  

p_v represent the p value

Hypotheis to test

We want to verify if the true mean is less than 25 min, the system of hypothesis would be:      

Null hypothesis:\mu \geq 25      

Alternative hypothesis:\mu < 25      

The statistic would be given by:

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)      

And replacing the info given we got:

z=\frac{24.25-25}{\frac{5}{\sqrt{100}}}=-1.5      

The p value for this case would be given with this probability:

p_v =P(z  

For this case since the p value is higher than the significance level of 0.01 we have enough evidence to fail to reject the null hypothesis and we don't have enough evidence to conclude that the true mean is significantly less than 25 min.

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55% = \frac{55}{100} = \frac{11}{20}

Multiply \frac{11}{20} by 80 and you will get how many boys play video games daily.

\frac{11}{20}*80=\frac{11}{1}*4=11*4=44

44 is the number of boys who play video games daily.

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A fish tank has black and white fish in the ratio of 2 to 6. Which is another ratio that can describe the black to white fish.
Ede4ka [16]
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Sunspots have been observed for many centuries. Records of sunspots from ancient Persian and Chinese astronomers go back thousan
Lunna [17]

Answer:

(a) Null Hypothesis, H_0 : \mu \leq 41  

    Alternate Hypothesis, H_A : \mu > 41

(b) The value of z test statistics is 1.08.

(c) We conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.

Step-by-step explanation:

We are given that in a random sample of 40 such periods from Spanish colonial times, the sample mean is x¯ = 47.0. Previous studies of sunspot activity during this period indicate that σ = 35.

It is thought that for thousands of years, the mean number of sunspots per 4-week period was about µ = 41.

Let \mu = <u><em>mean sunspot activity during the Spanish colonial period.</em></u>

(a) Null Hypothesis, H_0 : \mu \leq 41     {means that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41}

Alternate Hypothesis, H_A : \mu > 41     {means that the mean sunspot activity during the Spanish colonial period was higher than 41}

The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;

                            T.S. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean = 47

            σ = population standard deviation = 35

            n = sample of periods from Spanish colonial times = 40

So, <em><u>the test statistics</u></em>  =  \frac{47-41}{\frac{35}{\sqrt{40} } }

                                      =  1.08

(b) The value of z test statistics is 1.08.

(c) <u>Now, the P-value of the test statistics is given by;</u>

                P-value = P(Z > 1.08) = 1 - P(Z < 1.08)

                              = 1 - 0.8599 = <u>0.1401</u>

Since, the P-value of the test statistics is higher than the level of significance as 0.1401 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.

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Graph the function. Find the y-intercept and state the domain and range. Y = 3(2^x) - 4
Thepotemich [5.8K]

Answer:

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Step-by-step explanation:

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3 years ago
Round 436486.48649 nearest whole number?
Annette [7]
Its 436486  because you don't need to round it up
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