Question

Several years ago, the mean height of women 20 years of age or older was 63.7 inches. Suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 64.1 inches. (a) State the appropriate null and alternative hypotheses to assess whether women are taller today. (b) Suppose the P-value for this test is 0.06. Explain what this value represents. (c) Write a conclusion for this hypothesis test assuming an a

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Since the p – value is less than significance level . So, we will accept the null hypothesis.
​(a) State the appropriate null and alternative hypotheses to assess whether women are taller today.
Definition of null hypothesis : The null hypothesis attempts to show that no variation exists between variables or that a single variable is no different than its mean. it is denoted
Alternative Hypothesis : In statistical hypothesis testing, the alternative hypothesis is a position that states something is happening, a new theory is true instead of an old one (null hypothesis).
We are given that The mean height of women 20 years of age or older was 63.7 inches.
So, null hypothesis :  H₀ : μ = 63.7
Alternative Hypothesis :  H₁ : μ > 63.7
b)The​ P-value for this test is 0.06.
The p-value represents the probability of getting a sample mean height of 20 years old women is  64.1 inches.
c) Write a conclusion for this hypothesis test assuming an alpha equals 0.10 level of significance.
p- value = 0.06
Since the p – value is less .
So, we will accept the null hypothesis
So,
Hence The mean height is 63.7 inches