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Irina18 [472]
2 years ago
5

A social media platform states that a social media post from a marketing agency has 7 hashtags, on average. A digital marketing

specialist studying social media advertising believes the average number of hashtags used in a post from a marketing agency is different than the number stated by the social media platform. After completing a study, the digital marketing specialist found that the average number of hashtags used by a marketing agency in a social media post is 7.9 hashtags on average.
As the digital marketing specialist sets up a hypothesis test to determine if their belief is correct, what is their claim?
a. The average number of hashtags used in a social media post from a marketing agency is different than 7 hashtags.
b. The average number of hashtags used in a social media post from a marketing agency is different than 7.9 hashtags.
c. Marketing agencies use too many hashtags in a social media post.
d. The average number of hashtags used in a social media post from a marketing agency is 7 hashtags.
Mathematics
1 answer:
dimaraw [331]2 years ago
4 0

Answer:

a. The average number of hashtags used in a social media post from a marketing agency is different than 7 hashtags.

Step-by-step explanation:

A social media platform states that a social media post from a marketing agency has 7 hashtags, on average.

This means that at the null hypothesis, we test if the mean is 7, that is:

H_0: \mu = 7

A digital marketing specialist studying social media advertising believes the average number of hashtags used in a post from a marketing agency is different than the number stated by the social media platform.

Keyword is different, so at the null hypothesis, we test if the mean is different of 7, that is:

H_1: \mu \neq 7

Thus, the correct answer is given by option a.

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Laura has $1000 bond with a 3.4% coupon. Laura purchased this bond for $1065. What is the yield of this new bond?
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The XO Group Inc. conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of
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Answer:

a) 0.0392

b) 0.4688

c) At least $39,070 to be among the 5% most expensive.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 29858, \sigma = 5600

a. What is the probability that a wedding costs less than $20,000 (to 4 decimals)?

This is the pvalue of Z when X = 20000. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{20000 - 29858}{5600}

Z = -1.76

Z = -1.76 has a pvalue of 0.0392.

So this probability is 0.0392.

b. What is the probability that a wedding costs between $20,000 and $30,000 (to 4 decimals)?

This is the pvalue of Z when X = 30000 subtracted by the pvalue of Z when X = 20000.

X = 30000

Z = \frac{X - \mu}{\sigma}

Z = \frac{30000 - 29858}{5600}

Z = 0.02

Z = 0.02 has a pvalue of 0.5080.

X = 20000

Z = \frac{X - \mu}{\sigma}

Z = \frac{20000 - 29858}{5600}

Z = -1.76

Z = -1.76 has a pvalue of 0.0392.

So this probability is 0.5080 - 0.0392 = 0.4688

c. For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)?

This is the value of X when Z has a pvalue of 0.95. So this is X when Z = 1.645.

Z = \frac{X - \mu}{\sigma}

1.645 = \frac{X - 29858}{5600}

X - 29858 = 5600*1.645

X = 39070

The wedding would have to cost at least $39,070 to be among the 5% most expensive.

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