5. (10pt) (a) In how many ways can you choose a committee of 3 people from a gro
ID: 2946299 • Letter: 5
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5. (10pt) (a) In how many ways can you choose a committee of 3 people from a group of 12 people, if the order of selection matters? (b) How many outfits consisting of a pair of jeans, a sweater and boots does a teenager have if in her closet are: 3 pairs of jeans, 5 sweaters and 2 pairs of boots. 6. (10pt) Thirty percent of all the new houses built by The A-1 Construction Company fail the plumbing inspection. A random sample of six new houses built by this company is selected. Find the probability, to four decimal places, that exactly 2 failed the plumbing inspection. 7. (5pt) (a) For a given population of high school seniors, the SAT scores in mathematics are normally distributed with a mean score of 500 with a standard deviation of 100. Suppose that the engineering school will only accept high school seniors with a mathematics SAT score in the top 25%, what is the lowest score needed to be accepted into this program? (Spt) (b) Using the standard normal distribution find P(-0.12szs1.83), to four decimal places. (10pt) Suppose that the average person spends $8.40 per week on soft drinks, with a standard deviation of $2.70. A random sample of 45 people is taken. 8. (a) What is the mean of this sample? (b) What is the standard deviation of this sample? (c) What is the probability, to four decimal places, that the average amount spent on soft drinks by a person in this sample is between $8 and S9? 9. A soft-drink manufacturer claims that its 12-ounce cans contain, on average, no more random sample of 76 cans of this soft drink, which were checked for calories, contained a mean of 43 calories with a standard deviation of 3.2 calories. Does the sample information support the claim at a 1% significance level? (2pts) (a) State the null and alternate hypotheses. Identify which represents the claim. (Ipt) (b) Select the distribution to use: t-distribution or z-distribution (2pts) (c) Show the rejection and non-rejections regions of the distribution. (4pts) (d) Decide whether to reject or fail to reject the null hypothesis. than 42 calories. A (Ipt) (e) Write your conclusion in at least one complete sentence. 10. (10pt) A grocery store manager wishes to determine whether a certain product will sell equally well in D or E in the store. Five displays are set up, one in each location, and the resulting locations A, B, C, numbers of the product sold at each location are noted on the table below. Is there enough evidence that location makes a difference at the 10% significant level. Location A B C D E Number sold 41 32 5431 42 Page 2 of 2Explanation / Answer
Solution:-
9)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u < 42
Alternative hypothesis: u > 42
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.36707
DF = n - 1
D.F = 75
t = (x - u) / SE
t = 2.72
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 2.72.
Thus the P-value in this analysis is 0.008.
Interpret results. Since the P-value (0.008) is less than the significance level (0.01), we have to reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that its 12 ounce contains, on average, no more than 42 calories.
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