Question

**Confidence Intervals & Hypothesis Tests**

The manager of a restaurant wants to know if there is a correlation between the amount of a customer’s bill and the percent that they tip. In other words, as people spend more money, do they tend to tip at different rates? With data from a random sample of 157 receipts, he used StatKey to construct a 95% bootstrap confidence interval for r. The results were: [0.018, 0.292].

**A.** If the manager wanted to conduct a
hypothesis test instead, what would be the appropriate null and
alternative hypotheses?

**B**. Based on the 95% confidence interval, would
you expect the manager to reject or fail to reject the null
hypothesis at the 0.05 alpha level? Explain your reasoning.

**C**. Using this scenario, compare and contrast
confidence intervals and hypothesis testing. List at least one
similarity and at least one difference.

Answer #1

a) H0: there is no correlation between the amount of a customer’s bill and the percent that they tip

H1: there is a correlation between the amount of a customer’s bill and the percent that they tip

b) Zero is not contain in the given confidence interval. i.e. the populatin correlation coefficient value will be lies between (0.018 and 0.292). so we reject H0

c) Thus we conclude that there is a correlation between the amount of a customer’s bill and the percent that they tip

Is there a relationship between confidence intervals and
two-tailed hypothesis tests? Let c be the level of
confidence used to construct a confidence interval from sample
data. Let α be the level of significance for a two-tailed
hypothesis test. The following statement applies to hypothesis
tests of the mean.
For a two-tailed hypothesis test with level of significance
α and null hypothesis H0: μ =
k, we reject H0 whenever
k falls outside the c = 1 – α
confidence...

Is there a relationship between confidence intervals and
two-tailed hypothesis tests? Let c be the level of
confidence used to construct a confidence interval from sample
data. Let α be the level of significance for a two-tailed
hypothesis test. The following statement applies to hypothesis
tests of the mean.
For a two-tailed hypothesis test with level of significance
α and null hypothesis H0: μ =
k, we reject H0 whenever
k falls outside the c = 1 − α
confidence...

Is there a relationship between confidence intervals and
two-tailed hypothesis tests? Let c be the level of
confidence used to construct a confidence interval from sample
data. Let α be the level of significance for a two-tailed
hypothesis test. The following statement applies to hypothesis
tests of the mean.
For a two-tailed hypothesis test with level of significance
α and null hypothesis H0: μ =
k, we reject H0 whenever
k falls outside the c = 1
– α confidence interval...

A park manager wants to determine if the amount of support for
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1. What could be the potential research question for this
problem?
2. What could be the hypothesis and alternative hypothesis for
this problem?
3. Looking at the end-results of the T-Test that are here below,
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A market analyst wants to know if the new website he designed is
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with different designs. Assume that the data come from a
distribution that is Normally distributed. The data is shown in the
table to the right. Complete parts a through c below.
Website 1:
n1= 70
y1= 7.8
s1= 5.1
Website 2:
n2= 95
y2= 7.2...

Problem #1 Confidence Interval for Means using the t and
z Distribution. Psychologists studied
the percent tip at a restaurant when a message indicating that the
next day’s weather would be nice was written on the bill. Here are
tips from a random sample of patrons who received such a bill,
measured in percent of the total bill:
20.8 18.7
19.9 20.6
21.9 23.4
22.8 24.9
22.2 20.3
24.9 22.3
27.0 20.4
22.2 24.0
21.1 22.1
22.0 22.7
Open an...

The general manager of a chain of pharmaceutical stores reported
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thousands of square feet. Data for 14 pharmaceutical stores were
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The Reliable Housewares store manager wants to learn more about
the purchasing behavior of its "credit" customers. In fact, he is
speculating about four specific cases shown below (a) through (d)
and wants you to help him test their accuracy.
The average annual income of credit customers is less than
$48,000.
The true population proportion of credit customers who live in
an urban area exceeds 55%.
The average number of years lived in the current home is less
than 14...

1. For a pair of sample x- and y-values, what is the difference
between the observed value of y and the predicted value of y? a) An
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variable
2. Which of the following statements is false:
a) The correlation coefficient is unitless. b) A correlation
coefficient of 0.62 suggests a stronger correlation than a
correlation coefficient of -0.82. c) The correlation coefficient,
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