What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and
others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.† Suppose a random sample of n = 54 college students were surveyed and r = 9 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use α = 0.05.
1 answer:
Answer:
the questionnaire is incomplete, however the questions with the answers are left below and the used graph is attached
Step-by-step explanation:
a) What is the level of significance?
H0= P=0.240
Ha=p different 0.240
for 0.05 level z is 1.96
reject the null hypothesis if the absolute value of the statistical test results |z|>1.96
X=8.
n=59
Stderror=Se= √(p*(1-p)/n)=0.0556
P’= x/n= 8/59=0.136
Test stat z= ( p’-p)/Se= -1.87
P value = 0.0307
a) What is the level of significance?
significance level = 0.05
H0: p = 0.24; H1: \ neq 0.24
B. What sampling distribution will you use?
The normal standard, in this way we know that np> 5 and nq> 5.
sample test statistic value = -1.87 (try -1.88 if this goes wrong)
c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
P value of test statistic = 0.0307 (try 0.0301 if this goes wrong)
Regarding the distribution of the sampling, we analyze that the upper left curve is the right
D. Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
At ? = 0.05 level, given this result it can be concluded that the data are not statistically significant and that the null hypothesis cannot be rejected
E. Interpret your conclusion in the context of the application
thus, we conclude that at a level of o.05 there is insufficient evidence to report the proportion of university students who prefer the color blue when found at 0.24
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Step-by-step explanation:
Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;
The sum of an arithmetic series is expressed as
n is the number of terms
a is the first term of the sequence
d is the common difference
Given parameters
n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2
Required
Sum of the first seven terms of the sequence
The sum of the nth term of the sequence will be;
The sigma notation will be expressed as . <em>The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.</em>
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 and standard deviation
, the zscore of a measure X is given by:
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:
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
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
has a pvalue of 0.5080.
X = 20000
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.
The wedding would have to cost at least $39,070 to be among the 5% most expensive.